Couple of key things:

1. Camout. This is when the bit jumps out of the head of the screw, and scratches/damages the surface you are working on. It can also strip the screw head. It's almost impossible with star-head screws, but very common with cross-head (Phillips Head) and straight (flat head) screws.

2. Torque/Shear. A lot of people use drywall screws for everything. But it is easy to spin the head off the top of the screw (and leave the shaft in the wood) while mounting your cabinets on the wall. And those cabinets might fall down because drywall screws (and most phillips head screws) don't have much sheer strength, so the weight of the cabinet pressing down on the "neck" of the screw can shear the head off, and your cabinet falls off the wall with all your dishes in it. Star-head screws are (almost universally) made of tougher stuff with head and neck designs that are specifically made to stop shearing and carry those lateral loads better.

3. Standardization. No matter what you choose, standardize on it throughout your house. It is HUGELY annoying to have to use three different bits to remove a single light fixture. If you standardize and just keep one type of screw on hand, you will make and fix things with that one standard type of screw, and your life will get progressively easier over the duration of homeownership. (Related: I just spent an entire day going through my dad's workshop with him, and sorting a dozen different types of nails into a dozen different glass jars, and a dozen different screw types into a dozen other jars... and this man can't even turn a screwdriver anymore, due to age-issues with his wrist joints.)

4. Bits. Star-head screws always come with fresh bits in the box of screws. So you never need to buy another bit, and the ones you have are always fresh and new. It's a little thing, but... it's a big thing.

Finally, check out Steve Ramsey on YouTube. He does basic woodworking tutorials, and is great. This is his one about screws that got me on board with this way of thinking: