Question: quick question that's been bugging me lately. When it comes to a songs key specifically major and minor relatives- is it correct to say it can be written in two different keys with the same progression with the progression being written differently? I say this because a lot of times pop songs I see people post the progressions for, (usually 4 chord progressions that do not change during the song) some people list the major key and some list the minor key. For example lets use the song "Wake Me Up" -- A lot of people post the songs progression as a VI, IV, I, V and in the key of D. But other websites classify the song as in the key of Bm with the progression I, VI, III, VII.

My personal opinion would be that the song begins with Bm So I would say it's in the key of Bm following a I, VI, III, VII. If it had started on a D and modulated to Bm I'd say its in the key of D--- I'm I correct in saying this? Can you always class the song in two different keys since you can rewrite the progression differently but use the same chords? pls help :(

Answer: 
The song you quote with the bass line la,fa do,so and the chords Bm G D A can’t be identified as B minor or D major without listening to it.

vi IV I V is one possible solution referring to major (beginning on the 6th degree)

but this progression is ambivalent and it can be interpreted in Bm as i VI III bVII (b stands for the minor 7th degree of aeolian mode).

If we listen to the melody and we have somewhere a home feeling on each of these chords it may help us to decide whether the song is in Bm aeolian or in D major.

without a hint of tonic (see other answers): Yes it can be interpreted in both keys. But surely it makes sense to capital letters to assign Roman numbers of major chords and i, vi, for the minor chords.

If you have no other indications I agree with you that you say the song is in D as it begins with D.

But songs like this don’t need to be analyzed by R.N. It is sufficient that you know i VI ... in minor vi IV ... in major. You can practice this analogy back until to early Baroque music.
The answer to your question is **yes**.

The notation you use is relative to tonic. Establishing which sound is the tonic (and whether it changes) is completely outside of this tool. Consider anything noted as II-V as carrying a standard disclaimer "assuming that X is the tonic".

If you have a song with chords: C F C F C F, it might be a I-IV-I-IV, it might be a V-I-V-I. Depends on the rhythm, melody and even the listener. You can "make" yourself hear different tonics for the same progression in a similar way you can make yourself hear different "1" in a repeated drum loop.

There's some modern research concerning this, the classical theory just assumed that all people have roughly the same musical background and follow the same convention.