Ta’til means to deny and tajseem means to commit anthropomorphism (compare Allah to the creation). A mu’attil and a mujassim are, respectively, ones who commit those acts.
The gist of this rule is that the people who deny (ta’til) Allah’s Attributes do so out of a fear of commiting tajseem. They automatically conceive of the Attribute in an anthropomorphic manner and thus deny the clear, explicit meanings of the verses of Quran. In this process they compare Allah to other objects or non-existant, impossible objects and deny Allah of His perfect Attributes.
Those who actually do go so far as to commit tajseem make ta’til by denying the true meaning of the ayaat and denying Allah the Attributes He deserves.
The classical mujassimah (anthropomorphic) groups of Islam were, for the most part, Rafidah (shia) groups (although, in later times, the Shi’a are predominantly Mu’tazili). The non-Shia groups were primarily Sufis who believed that there was no existence except Allah (wahdatul wajood).
This is to contrast the Ash’aris who accuse Ahlus Sunnah now of being ‘anthropomorphic’. Note, these accusations against Ahlus Sunnah did not start until after the actual mujassimah groups died out.