Benrg's answer is really the correct one here, but I'd like to add a little historical perspective on why this convention exists. 3/4 meter generally represents 3 beats to a measure, where a quarter note is the primary beat. 6/8 generally represents 2 beats to a measure, where a dotted quarter is the primary beat.
To understand why this happened, it's useful to consider the older rhythmic notation of the renaissance, which ultimately led to our modern meters. We might consider four fundamental meters in renaissance music. (These were known historically as mensurations; see the table of "mensuration signs" in that link to see the historical notation I'm referring to in the following four meters.)
Let's assume that the whole note gets the beat (called a semibreve at the time, and still named that in many parts of the world). There was a desire to have groupings of two or three beats at a time, but also a desire to be able to divide up those beats into two or three subdivisions. Four possibilities emerge:
- We could have a situation where there are 2 whole notes per major grouping (i.e., 2 beats), and each whole note is divided into 2 smaller notes (called minims, the ancestor of our modern "half note," but that latter name is misleading, as we shall soon see)
- We could have 3 whole notes per major grouping, each divided into 2 minims
- We could have 2 whole notes per major grouping, each divided into 3 minims (perhaps the minims here could be thought of as "third notes" instead of "half notes")
- We could have 3 whole notes per major grouping, each divided into 3 minims
Effectively, options (1) and (3) have two beats per group ("measure" in our modern parlance), while (2) and (4) have three beats per measure. And options (1) and (2) have beats that are subdivided into two parts, while options (3) and (4) have beats that are subdivided into three parts.
Originally, all the "whole notes" looked alike, and you just had to know based on the meter when you were expected to count 2 minims per whole note vs. 3 minims per whole note. Similarly the next higher level above whole notes (breves) all looked alike too, and you just had to keep track of how many whole notes (semibreves) per breve.
But note something: triplet notation had not been invented, at least not as we use it today. So a "whole note" had to do double duty in a situation when it was divided into three parts: sometimes it was held for the full three count, and other times it was reduced to only two subdivisions, when followed by a minim. There were a huge amount of rules about when some notes were read one way or another way -- in different circumstances, the exact same note shape could stand for a value that was twice as long or twice as short or sometimes more exotic ratios.
By the 1500s, those triple subdivision meters were starting to die out in favor of a standard meter that looked like option (1) in the above list. In own modern system, we might call that meter 2/1, as it had two primary beats to a bar, with each beat divided into two parts. Rather than having notes that could look like they were sometimes longer duration and sometimes shorter, the option (1) became the standard used for meters even with groupings of three.
So, for options (3) and (4), each "minim" literally became a "half note," and the primary "beat" would now be notated as a dotted whole note, instead of the previous notation where the "whole note" (semibreve) could change its division based on context.
This was seen as a great simplification, but it led to a problem: how to indicate "compound meter" like in (3) and (4) above. (1) and (2) could be notated as 2/1 and 3/1, but in option (3) there are only two beats and the whole note doesn't have the beat.
The compromise that was eventually adopted was to go down one level in duration and use that for the denominator of time signatures, assuming that the 6 or 9 (and later 12) in the numerator would be assumed to represent a threefold division of the primary beat.
Hence, our four options could be represented using modern meter signatures as: 2/1, 3/1, 6/2, and 9/2.
Over the time that this was becoming standardized, however, there developed a preference for "black note" notation with shorter durational values. So these four options eventually became standardized at a quarter of their original length, i.e., 2/4, 3/4, 6/8, and 9/8. They represent the same concept of beat groupings and subdivisions as the four situations listed above, just now with a quarter or dotted quarter getting the primary "beat."
From a historical perspective, 6/8 is a "compound meter" because it was the simplest notation possible to capture the fact that it was distinct from 3/4 because the beat fell on the dotted quarter. If there were a way of representing 2/♩., that could be used instead as that was literally the situation that 6/8 was chosen to represent. Instead of using 2/♩., however, they chose a mathematical shorthand that started to generate confusion once the old system of meters died out and people forgot that 6/8 didn't mean "six beats per bar," but rather only two.