3/4 means there are three/quarter notes to a measure.
The tempo mark will usually say how many quarter notes to a second since you are saying how many quarter notes to a measure in the time signature.
If you changed the time signature to 4/8 time (four/eighth notes to a measure), it is typical then to say how many eighth notes to a second in the tempo mark.
So, no, it will not change your tempo going from 3/4 to 4/4, however, 3/4 to 3/8 would change things.
But, what 3/4 and 4/4 will change is the beat. 3/4 you would count 1,2,3,1,2,3 (with an accent on the 1 in most cases). But in 4/4, the way the beats are counted changes to 1,2,3,4,1,2,3,4 because now you have 4 beats to a measure. edit: Also, the measure bar lines should always be right before the 1, so if you change from 4/4 to 3/4 then you would have more bar lines and they would mostly all have to move.