They are both commonly used and have related, but distinct, meanings. Floppy = not stiff, not standing upright. Many dogs and goats have floppy ears, a soft hat with a big brim is floppy, clothes that are too big for you are floppy. In general, this word is used to describe things, not people. "Floppy" isn't necessarily bad or good. Flabby = being overweight and unfit (in the athletic sense), having loose skin and fat. This usually applies only to people and is insulting. I hope that helps!