English distinguishes auxiliaries and modal verbs. Auxiliaries (to be, to have, to do) combine with present participle or past participles or infinitive to form the verb forms of ordinary verbs. Modal verbs combine with infinitives to express ability, probability, necessity, permission, obligation, deduction etc.

was-were can, could, to be able to
has-have-had will, won’t, shall, shan’t
to have to will,would, shall, should
short yes/no answer modal mix: (can, could, may, might, must, had to, ought, shall, should, will, would)
tag-questions modalities: ability, permission, probability, deduction, necessity, request and obligation