Quarter Round v. Shoe Moulding
The terms can be used interchangeably, but there is a difference. First, why do you use moulding at all? This is often used to finish out trim, perhaps for appearance or otherwise for necessity in case the floor doesn’t quite “go far enough” under the baseboard. It it optional to put on as long as your floor extends to or below the baseboard. Personally, I have mixed feelings about it. It’s one more thing to clean and get beat up by shoes, the vacuum, etc. However, it can added a richer look to the trim, so it’s a matter of opinion and may depend on the room.
If you decide (or need) to install it, I like the shoe moulding better. It is a little thinner, more flexible to work with and has a “less chunky” look to it in my opinion. Get a piece of both from the hardware store and hold it up to your baseboard and decide which you like better.
Pro Tips:
Paint before installing
Fill nail holes after installation
Caulk top of moulding where it meets baseboard, but not below.