A catenative verb is a helping verb. Specifically, it's part of the verb phrase and it is not an auxiliary. It is followed by another verb which functions as the main verb in the verb phrase. Catenatives may have aspectual meanings, denoting the start, unfolding, or end of an action (e.g., stop running, get to like, continue to read), or modal meanings such as certainty and usuality (seem to like, appear to be, tend to occur). Finally, the catenative get may be a marker of the passive voice (get married, get paid). Read more here .
A predicator is the verb in its functional relation to the clause. It is comparable to the grammatical relations of subject and object.
The term predicator can be used to refer to the verbal element in Subject-Ver b-Object constructions, that is, Subject-Predicator-Object. This avoids the confusion of using verb to refer to both a form and a function. Read more here.