I'm badly confused between modal and auxiliary verbs. What are the differences?
Modals are a subclass of auxiliaries. All modal verbs are also auxiliary verbs, but not all auxiliary verbs are modals. The auxiliaries not conventionally included among the modals are be, have and do - all of which double up as full verbs.
The modals have various shared characteristics - they don't have a separate third-person singular ending and they don't have infinitives or participles. Be and have have infinitives and participles, even when fulfilling their auxiliary functions (e.g. "to be seen", "to have seen"), which is one of the reasons for classifying them differently.
The modals are can, may, will, shall, must, ought. The semi-modals are need and dare (which do have infinitives and participles), and arguably one or two others (depending which book you read). (Also, ought is sometimes classed as semi-modal instead of modal, because of its particular characteristics.)
Could, might, would, should are sometimes listed as modals, although really they are the past-tense forms of can, may, will, shall, so don't need to be listed separately.