Completely different roles. The APC is designed to provide its occupants with supporting fire against opposing infantry and very light armor. It is designed to get its occupants to the battle quickly and remove them from the battle quickly. The primary combatants are still the infantry in it.
A tank is designed to destroy opposing armor. They are not well suited to dealing with infantry and its occupants are not intended to take on other infantry themselves. They are also heavy, slow, and a pain in the ass to transport to the war zone.
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