Is there any difference between playing in 3/4 and 6/8?
Yeah, you count it differently. 3/4 goes 123, 123, 123, 6/8 goes 123456, 123456, 123456. Emphasis on that 4th beat.
We're only strays.
6/8 is triple meter. 1st and 4th beats are emphasized. every other beat is an 8th note instead of a quarter note. 8th notes are in groups of 3. 3/4 is double meter. each beat represents a quarter note. 8th notes are in groups of 2 or 4.
RIP George Carlin (1937-2008)
Tip: Don't look at time sigs like mathematical fractions. They're nothing like that.

You'll love this: http://www.musictheory.net/lessons/html/id15_en.html

Check out the other ones too.
“Science cannot solve the ultimate mystery of nature. And that is because, in the last analysis, we ourselves are part of nature and therefore part of the mystery that we are trying to solve.”

-Max Planck

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the pulse of 6/8 is two dotted quavers per bar .
where as with 3/4 its 3 straight quavers .
research "pulse" i think you will find the answer there