I'm going to use the British note-duration names, because I think (certainly at times like this) they are less confusing. In 3 4 time the beat isn't a 'quarter' of anything; it's far easier to say "3 4 time is 3 crotchets per bar"
Here are some normal bars in 4 4 time:
X:1
K:C
M:4/4
L:1/4
V: voice
C C C C | D D D D | E E E E ||
You ask
Is 3 on 4 like playing 3 notes in a 4/4 piece?
Yes, it's exactly that:
X:1
K:C
M:4/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(3:4:3 C C C | (3:4:3 D D D | (3:4:3 EEE ||
V:LH clef=bass
C, C, C, C, | D, D, D, D, | E, E, E, E, ||
Those treble clef notes are written as crotchets, but the 3 above is an instruction that they are 'out of time', and you have to look at the context to understand the total time they occupy
And does 4 on 3 mean you play 4 notes in for example 3/4?
You've got it. Here are some normal bars in 3 4 time:
X:1
K:C
M:3/4
L:1/4
C C C | D D D | E E E ||
And here is some "4 on 3" :
X:1
K:C
M:3/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(4:3:4CCCC | (4:3:4DDDD | (4:3:4EEEE ||
V:LH clef=bass
C, C, C, | D, D, D, | E, E, E, ||
Typically all such constructs are found only briefly in the middle of otherwise 'in time' music:
X:1
K:C
M:3/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
CCC | (4:3:4DDDD | EEE ||
V:LH clef=bass
C, C, C, | D, D, D, | E, E, E, ||
but there's nothing to stop someone writing an entire piece like this:
X:1
K:C
M:5/4
L:1/4
%%staves {(RH) (LH)}
V:RH clef=treble
(7:5:7CCCCCCC | (7:5:7DDDDDDD | (7:5:7DDDDDDD ||
V:LH clef=bass
C, C,C,C, C, | D, D, D,D, D, | E, E, E, E,E, ||
