Princeton review says
"fungi misses chlorophyll thus it's heterotrophs"
the other book says
"fungi misses chlorophyll thus it's thallophytes"

which one is correct?

I can't even find the word thallophytes from fungi outline :(

try looking the word thallophytes up...it's just another word for a group of organisms that once got classified with pants but later on people figured out it wasn't a good classification.

both statements you have there are true. In bio, there are often more than one reason something can be true