There is a great deal of difference between an animal companion "familiar" and that which is purely rooted in the spiritual, in my opinion. Particularly if such is a created entity.
If I may be frank, most folks who have such an animal companion have a warm bond with a pet. This is not so different than any other experience one might have with a beloved animal, but the individual simply sees it as more than this. Sometimes there's a bit more to this but, well... to each their own.
Familiars and the like of the spiritual variety, including created servitors/homunculi/etc., are generally more in line with the traditional lore (despite the cat familiar being what is most commonly depicted), presenting bond between the magic practitioner and a being that work together within one's magical practice.