They're pretty much equivalent.
That said, omitting the article has a slight feeling of playing with a group or orchestra, wherein the instrument is a synecdoche referring to the position the person occupied within the group.
I used to play the flute.
I used to play flute in the Civic Orchestra.
Omitting the article also can carry the feeling of playing an instrument in the general sense.
I play woodwinds.
In this case it would sound strange to use the article because you are speaking of a class of instruments.
english.stackexchange.com/users/2303/Robusto
I remember when I first moved from the UK to the US, I was quite taken aback by the “I play piano” usage, without the article.
So I’m pretty sure that this usage is very uncommon in the UK (at least among classical music circles).
In US usage, Robusto’s answer, that the article-less usage is more common in reference to playing with a particular group, fits my experience (classical groups, north-east US) pretty well.
english.stackexchange.com/users/2587/PLL
Articles are creatures more of usage and discourse than of grammar.
The human speech communities involved (UK vs US; musicians, cooks, scientists, etc.) have certain patterns and expectations for use in the domains they control.
The surrounding text (conversation or writing) also guides usage.
As an American, I accept using or omitting the article before an instrument; they are nearly interchangeable for me.
I like the idea above that the article-less usage stresses playing with a group and the article usage stresses the position within the group.
As an ESL teacher, I have generally taught that omitting the article highlights the action or activity, almost as if practicing-violin were a single intransitive concept, like swimming.
Using the article gives a subtle shift in focus to the instrument.
The following is a sentence I would be likely to produce; I would accept any version of this (article-wise) that I might
hear:"When
he was little he played violin, but he switched to the cello when he got to middle school."
english.stackexchange.com/users/10377/Janet
I heard somewhere that if the instrument is big and can hardly or even can't be carried (like cello, piano, drum set, harp, grand-piano, organ, etc.)
the definite article is needed.
I am not sure if that's correct, though.
english.stackexchange.com/users/2270/brilliant
I play piano??
This is I understand an American usage and is unacceptable in British or Australian English.
I play strings
I play drums
This is the usual option to omit the (indefinite) article - it means you play instruments in this category but doesn't mean you play all stringed instruments (or whatever), but that you play some (and the implication is a few).
The drums is a bit of a special case plural representing a singular set of drums or a number of different percussion instruments.
If you play a number of different percussion instruments in an orchestra you would normally play drums and other percussion instruments and refer to percussion.
The drum set in a band (which also includes non-drum percussion components - big hat, cymbals, etc.)
is actually a stand in for the whole percussion section in a full orchestra, so the "role" usage I suggest below prevails.
I play percussion
I play woodwind
I play brass
These are actually an adjective with an implicit "instruments" omitted, so it looks like a mass noun and doesn't have plural -s, but otherwise acts like the "strings" case above.
I'm intrigued by the @brilliant idea that it has to do with being portable.
I think the indefinite usage has more to do with playing a particular role in an ensemble or orchestra where there are multiple instruments playing the X part
(implicitly plural even if singular in form), rather than a unique role (so definite singular).
Thus it is appropriate to say I play X (meaning the role and the part as well as the instrument).
These is confirmed by it being easier to omit the article when the "in the orchestra" or similar is explicitly or implicitly present.
I can say
I play cello
I play trombone
I play guitar
I play banjo
I can't say I play piano??
I play mandolin??
I play harp??
The mandolin is portable.
But there are not often multiple of any of these in a typical modern band, ensemble or orchestra.
Piano and harp fit both theories.
english.stackexchange.com/users/39262/David M W Powers
I actually play the mandolin in a group and it is a small light instrument that can be very easily carried in a small case, more easily than a guitar so this argument is not good enough.
I agree that "I play mandolin" seems to be a modern way of saying "I play the part devoted to the mandolin in this group".
"I play the mandolin" is the best way to specify which instrument I play and the normal classical English usage.
english.stackexchange.com/users/128470/Joelle Cadennes
"I shoulde'v learned to play the guitar, I shoulde'v learned to play them drums" - Dire Straits.
I would definitely go for " the piano ".
In fact the first sentence sounds strange.
english.stackexchange.com/users/120679/Konrad Gajewski
Difficult to give basic rules.
One idiomatic use with the definite article is
I'm learning to play the piano.
Longman DCE.
english.stackexchange.com/users/63507/rogermue
What is the rule for omitting/including the definite article in the following sentences:   I used to play piano.   I used to play  the  piano.   I would pick the first sentence, but I've heard people say the second sentence even when they are not referring to a specific piano.Which one is correct?
Omission of definite article with musical instruments
english.stackexchange.com
<definite-articles><zero-article>
english.stackexchange.com/questions/6635
english.stackexchange.com/users/2745/YGL
It is hard to give basic rules but it is generally agreed that the two forms are equivalent. Having said this, omitting the article may refer more to playing with a group or orchestra. It is also possible that there is a difference between UK and US English, with UK English preferring to use the article. There is not much difference though the consensus is the removing the article suggests playing in a group, whilst the article creates a focus on the instrument  played. Nevertheless , choices may differ between English speakers as well as within groups of people working in a particular domain, such as musicians.It is surprising for US speakers not to hear "a".The grammatical overtones of the article might add focus to the instrument. Individuals within certain groups may have specific speech patterns they use related to their domain.
It is hard to give basic rules but it is generally agreed that the two forms are equivalent. Having said this, omitting the article may refer more to playing with a group or orchestra. It is also possible that there is a difference between UK and US English, with UK English preferring to use the article. Although they are both used, some feel that the definite article is required.
Although widely interchangeable, some people perceive a slight difference between these phrases. Using the article gives a subtle shift in focus to the instrument. Omitting the article also can carry the feeling of playing an instrument in the general sense, or with am orchestra, for example. These two constructions might be interchangeable and it is difficult to describe any basic rules. However, it is possible that omitting the article is more common when referring to playing as part of a group. Similarly, omitting the article may place more emphasis on the activity rather than the instrument.
There is not much different. Removing the article might suggest having played with an orchestra. It is surprising for US speakers. The grammatical overtones of the article might add focus to the instrument. Individuals within certain groups may have specific speech patterns they use related to their domain. It is usual to omit the article. It simply means you play the instrument in this category or at least some of them. "Drums"as a plural presents a special case.
They mean the same thing. The definite article is needed.
It is possible that omitting the article is used when referencing playing an instrument as part of a group. Omitting the article could place more emphasis on the activity rather than the instrument. It is difficult to give any basic rule. These two constructions might be interchangeable. 