I’m guessing you understand the difference between duple and compound time(?) but just in case:-
4/4 means there are four crotchet beats to each bar. The main stress is on beat 1. There is a smaller stress on beat 3 and beats 2 and 4 are weakly stressed.
6/8 means there are six quaver beats to a bar. The main stress is on beat 1. There is another stress on beat 4. All other beats are weakly stressed.
Consequently, 6/8 is more like 2/4. Indeed, a 6/8 bar can be written in 2/4 using two groups of triplet quavers.
TWO bars of 6/8 could be written as ONE bar of 4/4 (though they would sound different rhythmically in performance). The difference is subtle but it’s there.
When conducting 6/8 it is sometimes convenient and easier for the orchestra to read if it is done as TWO dotted crotchet beats to a bar with each beat divided into THREE quaver “sub-beats”, 1 2 3 2 2 3… This is different to 2/4 time which is also TWO crotchet beats. 1 2 2 2 1 2… If it is necessary to divide this beat, it will be divided into TWO quavers.
Hence 2/4 (and 4/4) are simple duple time whilst 6/8 is compound duple time. They feel thymically very different. The beat unit in simple duple time is the crotchet, the beat unit in compound duple time is the dotted crotchet.
Note when doing the maths that 6 quaver beats per bar is NOT the same as 3 crotchet beats per bar (which is 3/4); rather it is equivalent to 2 dotted crotchet beats per bar (as above).