The difference, in one paragraph
Acrylic is a powder and a liquid mixed into a bead at the table and shaped before it sets. Hard gel is a thick gel built in thin layers and cured under a lamp. Acrylic is harder, cheaper and quicker; hard gel is lighter, flexes with the nail rather than against it, and does not fill the room with a smell. Acrylic can be soaked off. Hard gel cannot — it is filed off, which is why the removal takes as long as it does.
A fill is a rebalance, not a top-up
At two to three weeks the regrowth at the base has moved the stress point of the whole nail down towards your fingertip, and that is when nails start breaking at the side walls. A fill takes the existing product down, fills the new growth and rebuilds the apex where it should be. Past about five weeks the set has usually travelled far enough that a fill is the wrong appointment, and we will tell you that with the price difference before we start rather than halfway through.
Length and shape cost the same
A short square set and a long almond set are the same price. The work is the same work; the length of the nail is your decision, not a surcharge. What we will say honestly is that a long set on somebody who works with their hands all day is a set that will break, and that is worth ten seconds of conversation before we start.
It is not the acrylic that damages the nail
It is the removal, and mostly it is the removal you do yourself at home in front of the television. There is a page on this site about exactly that, because it is the single most useful thing anybody in this trade can tell you.