These words have different meanings, although both are connected to groups of people or things gathering together.
Hoard can mean “a collection of something stored up” (noun) or “to collect and save something” (verb). It connotes possession and possessiveness; a dragon’s hoard is the most famous cliché. And during the COVID pandemic there was a problem with people hoarding toilet paper.
Horde appears only as a noun and can describe any large group of people. Originally it referred to nomadic tribal people from Mongolia. But today it is common to refer to any large group of people gathered together as a horde, i.e., a crowd.