Both 3/4 time and 6/8 time work out to the same length of time, so what's the difference?
Since 3/4 is a bar of 3 quarter notes, and 6/8 is a bar of 6 eighth notes, they both last the same amount of time. However, they have some subtle difference.
First of all, a 3/4 bar implies the bar will be centered around usage of quarter notes, while 6/8 implies usage of eighth notes.
More interestingly, though, 3/4 time implies a strong beat falls 3 times per bar, while 6/8 time implies a strong beat falls twice per bar, once at the start of each group of 3 eighth notes. Have a look at the difference below.
It's a subtle distinction, but as you get exposed to more songs in 3/4 and 6/8 time, you'll be able to feel the difference.