I have cotton threads on cones like those. The serger thread cones are normally fatter at the bottom and taper in as it goes to the top. Also, most serger thread is not a consistent weight. Pull a few inches off and you can tell if it is serger thread by the thinness then fatness of the thread.
A way that I try to check & see if it is polyester is to pull it and try to break it. Most polyester thread I have seen takes longer to break than the cotton. It also melts easier.