They're all soft, mild, fresh cheeses (meaning they're eaten young, not aged), which is why they get swapped around. But they're made from different things in different ways:

• Ricotta is made from whey, the liquid left over from making other cheeses. The name means "recooked," because the whey is heated again until the last bits of protein form soft, fluffy curds. That's the filling in lasagna and ravioli.
• Mascarpone is an Italian cheese made from cream, with a very high fat content, so it's rich and smooth enough to spread. It's famous as the base of tiramisu.
• Cottage cheese is cheese curds that haven't been pressed, so it stays chunky and wet. It comes in a lot of varieties depending on the fat level and milk used.
• Cream cheese is a mild, slightly sweet, spreadable fresh cheese. Think bagels, spreads, frostings and cheesecake.

Can you swap them? Sometimes. Cottage cheese stands in for ricotta in a lot of desserts, and mascarpone works as a richer substitute for ricotta in baked pasta. Cream cheese is the odd one out, since it's tangier and denser, so it doesn't behave like the others.

Related: What is whey and what can I do with it? · How do you make ricotta from whey? · What is paneer, and is it the same as ricotta? · What do I need to make cheese at home?