TL;DR: Generally speaking, the mixer faders should be used for mixing only (which may include solving technical problems, but not “musical” dynamics), whereas velocity and dynamics (modwheel) should be used for musical expression.
Sidenote: You could also use the mixer faders for balancing instruments in the mix, if they don’t come with the correct gains out of the box (usually the case when combining unrelated libraries, but some libraries don’t even have the instruments balanced in the first place), but I think it’s better to use the sampler output gain, mixer pre-gain adjustment or similar for that, so that “all faders at 0 dB” is the starting point when you get into actual mixing. Technically speaking, it doesn’t matter at all, though - unless you have non-linear plugins (compression, saturation, tape simulation, waveshapers…), which will of course be affected if you change the gain before them.
The dynamics implementation varies between instruments, but typically, short articulations will be velocity controlled, whereas long articulations are modwheel controlled. Some use both, for separate control of onset and sustain. These controls will generally switch/fade between sampled velocity layers, apply filters and whatnot, to create a realistic impression of actual dynamic playing. For most instruments, this is very different from just changing the volume!
Some sample libraries also have two confusingly named controls (Dynamics and Expression, in the case of most/all Spitfire libs, for example), where one is the actual dynamics control (sampled layers etc), and the other is essentially just an extra volume control, for when the dynamic range of the sampled layers isn’t enough. The later should only be used as a last resort, or for special effect, as it’s not very realistic.
Some libraries (some 8Dio ones, for example) allow these “true dynamics” and “secondary volume” controls to be linked, for increased dynamic range.
Other libraries (Orchestral Tools etc) have a Niente switch somewhere, which applies extra “fake” dynamic range, so that velocity/dynamics scales all the way down to silence, rather than the recorded level of the quietest sample layer.