No real conflict there. It's not so much inverting to get the voice leading, it's more about rrevoicing the chord so that 3rds and 7ths do their thing. And/or other notes don't jump around so much. Very often it means the bottom note of their chord has changed so no longer a voicing with root at the bottom, so you could say it is also an inversion as well as rearringing of other notes, but it's more a by product of the revoicing.
As a evry simple example go to a keyboard and play a C triad (CEG) followed by F triad (FAC) just like that in root position.
You will see all the notes moved up a fourth (or down a fifth).
Now, instead of that play C as before but the F as CFA, so the C remains where it is, the E moves up to F (strong voice leading) and the G up to A (not really the same kind of voice leading but a small movement)
It's called voice leading because this kind of movement of the notes between two chords is much easier and more flowing for singers, it comes from choral writing, hence "voices"