No, they're different cheeses, though both are fresh and mild.
Paneer is a fresh, acid-set cheese native to the Indian subcontinent. It's made by curdling milk with something acidic, usually lemon juice or vinegar, then draining and pressing the curds. It's a little like pressed cottage cheese. Because it's pressed, it's firm and holds its shape when cooked, which is why you can cube it and fry it or simmer it in a curry like saag paneer.
Ricotta is made from whey, the liquid left over from making other cheeses, which is heated again until the last bits of protein form soft, fluffy curds. It's creamy and delicate rather than firm.
So paneer is made from milk curds and is firm, while ricotta is made from whey and is soft. Paneer is also one of the easiest cheeses to make at home, with just milk, lemon juice and cheesecloth, which makes it a great first cheese.
Related: What is whey and what can I do with it? · How do you make ricotta from whey? · What is the difference between ricotta, mascarpone, cottage cheese and cream cheese? · What do I need to make cheese at home?