A stain is of any shape or size. A spot refers to a small stain, usually circular. "Spot" can also mean "place", as in your second example. We say things like "This is my spot" to let someone know they are sitting or standing in the place we had already chosen for ourselves. We say "Mind my spot" to ask a friend to look after our place (for example, in a queue) while we go for a short time to do something else. I hope that helps!

"Spot" emphasizes the idea of a small place, a small region, or a dot. "Stain" emphasizes the idea of discoloration. It often carries the idea of dirt, defilement, or corruption. A stain that is confined within a small area can be called a "spot." If we spill coffee all over a white tablecloth and turn a large part of it brown, that's "a stain" but not "a spot." If we spill a single drop of coffee on a white tablecloth, we might call the result either "a spot" or "a stain." If a mosquito bites us and it creates one specific place where it itches, we have "an itchy spot." That's a "spot" that is not a "stain."

I agree with the first answer and add that stain means a discoloration, while spot can be a normal coloration. Example:. Leopards have spots, not stains.