Mechanical damage, the kind caused by a doorknob, a piece of furniture, or a foot through a garage wall, is almost always a patch. The board around the hole is still sound and still dry. We cut back to a clean rectangle, back it properly so the patch can't move, tape, coat, feather the joint out wide, and match whatever texture is on the rest of the wall. Done right, it disappears under paint and you'll lose track of where it was.
Water damage is a different question, and the answer depends on what the board feels like. Drywall that got wet and dried quickly can be fine: a stain, maybe some chalking, and a coat of stain-blocking primer handles it. Drywall that stayed wet has lost its structure. If it's soft, if the paper has separated from the gypsum, or if it crumbles when you press it, no amount of mud fixes that. It comes out.
The part people skip is finding out why it got wet. Replacing a ceiling under an unrepaired roof leak is paying twice for the same job. We trace the source first, whether that's flashing, a vent boot, a supply line, or condensation from poorly insulated ductwork in the attic. If it's the roof, we're already the people who can fix it, which saves you a second contractor and a second schedule.
Anywhere you suspect mold, treat the drywall as disposable. Porous material that has grown mold doesn't get cleaned and sealed, it gets removed, and the cavity behind it gets dried out before anything new goes up.
Matching texture is the step that decides whether a repair looks like a repair. Knockdown, orange peel, skip trowel, and smooth all behave differently and all need a sample board and a little trial and error to match. It's worth the extra half hour. A perfectly flat patch with the wrong texture is more obvious than the hole was.