Simple and compound meters - I'm confused

[linglingwannabe]

 In musical notation, there are many ways to represent the same sound (ex.: two half notes = one whole note etc.). Conversely, each time signature can be classified into a certain meter, meaning it has a specific number of beats, which can be broken down in a certain number of notes, forming duples, triples, quadruples and etc.
 But take 6/8 time, for example: it can be represented as 6 8th notes, two dotted quarter notes (forming a compound duple) or as 3 quarter notes (forming a simple triple). Are there any differences when you play each of these forms on the piano?

[brogers70]

Sure there are differences. In your 6/8 example, you'll feel the rhythm differently if count count two beats to the measure, as opposed to 6; counting 6 eighth notes will tend to make your playing kind of square and not very fluid. So then imagine you are counting 2 beats (ie a beat is a dotted quarter) to the measure and you switch to counting 3 beats to the measure (ie a beat is a quarter), you'll have a hemiola, and you'll definitely feel the difference. The eighth notes will still each get the same amount of time, but the pulse will feel very different.

[quantum]

But take 6/8 time, for example: it can be represented as 6 8th notes, two dotted quarter notes (forming a compound duple) or as 3 quarter notes (forming a simple triple). Are there any differences when you play each of these forms on the piano?

Three quarter notes in a time signature of 6/8 is an example of horizontal hemiola. 

Regardless of what instrument it is being played on, there is a difference in how this sounds.  Compound duple has has two beat groupings per bar, with each group subdivided into three.  Simple triple has three beat groupings per bar, with each group being subdivided into two. 

The differences are where emphasized beats are placed and how you subdivide the main beats. 

[j_tour]

Three quarter notes in a time signature of 6/8 is an example of horizontal hemiola. 

Regardless of what instrument it is being played on, there is a difference in how this sounds.  Compound duple has has two beat groupings per bar, with each group subdivided into three.  Simple triple has three beat groupings per bar, with each group being subdivided into two. 

The differences are where emphasized beats are placed and how you subdivide the main beats.

I don't have anything to add, but I just wanted to say that's one of the best explanations I've heard.

I'll be borrowing your style when, for example, trying to say how 12/8 is to be played.

It's pretty difficult to explain in words.  Easy to play or feel, perhaps, but it's difficult to explain. 

But you managed, and I would say very well.