Fakes are something someone put together and claimed to be something it's not. The difference between a fake and a bootleg is that bootlegs are sold in large quantities in stores, flea markets, toy shows, and/or etc. Fakes tend to be made in very low quantities (or one of a kind) by one or a few people on their own. While bootlegs are collectable, I don't know of anyone that collects fakes. Below is an example of a fake. It's just some plastic molded to look like a vintage Amanaman figure. It was then sold at a toy show where the seller claimed it was a prototype figure. The buyer of this toy got ripped off.
Unlike a real prototype, this one is brittle and there are gaps where the edges should fit together.
Customs are made by modifying another piece with clay, paint, and/or other elements and techniques. Some are made to create an item that someone wants but has yet to be made by Hasbro, Kenner, etc.. Others are pieces that someone puts together to resemble another piece, although they don't claim it to be the real deal. Here's a Kenner Jawa that an action figure customizer outfitted with a cut sheet of plastic, trying to make their own vinyl cape Jawa (a VERY sought after vintage Star Wars figure variation).
The customizer meant no harm when they made this figure, and wasn't trying to fool anyone. This is just a fun item to own because it's like a placeholder for a collectible that doesn't come around too often.
Homemade pieces are just that; a piece made at home (or somewhere outside of a factory). They're like a craft project from scratch. A homemade item can sometimes crossover with the custom category. Here's a clay R2-D2 figure that a parent made for their son.