Question: Some islands are called isle like "Isle of Man", "Isle of Tortuga" and the "British Isles". Other islands are called island, like "Island of Malta" or "Island of Cyprus".

What is the difference between the words?
How to know if a land mass confined by water is called an isle or an island?

Answer: 
In modern everyday use 'Isle' tends to be included in the name by which the place is known, such as the ones you mention plus the Isle of Skye, Isle of Mull, Isle of Wight etc. (No one says simply 'Wight' to refer to the Isle of Wight, nor 'Man' to refer to the Isle of Man.) Though you may hear the term 'island of Malta', or island of Cyprus', which are quite correct since both are islands - the word 'island' does not usually form part of the place name, by which they are called. One would normally say simply 'Malta' or 'Cyprus'. You would only use the word 'island' if you were wanting to stress the fact that they were islands. which is why I have not capitalised the i.
There is no difference in the words' meanings, they both denote a landmass surrounded by water.
The [definition](http://www.thefreedictionary.com/isle) from one of the dictionaries sums it up nicely about "isle", I think:

> 
> Poetic except when cap. and part of place name; an island, esp a small one
> 
> 
> 

So "isle" has the same meaning, just more poetic (it is a monosyllabic word), more often used with small islands. As for geographic names - they were named like that at some time, so someone chose "isle" over "island" while naming them.