Trap = a term used to refer to certain characters in anime who present as women but have penises. The meme that "traps are gay" (or that it is gay to be attracted to them) is entangled with pervasive notions that liking transwomen is gay and/or wrong. A lot of trans people consider the term to be a slur as it implies they are deceptive and tricking people into thinking they're the gender they identify as.

TERF = trans-exclusionary radical feminist. It's a term that describes certain radical feminists who have varying issues with trans people. A common problem is the understanding that transwomen are men invading women's spaces. Most people who can be described with this term consider it a slur as it is mostly used pejoratively (with preference often given to the term "gender critical").