Funeral is a noun, and funereal is an adjective—they are the same word in different forms (different parts of speech).
A funeral is the ceremony we have after a person has died, which ends with the burial or cremation (burning). The funeral is not the act of burying or cremating the body, but rather the whole ritual, which often begins in a church or temple and ends in a cemetery.
Funereal, as an adjective, has two meanings. It can simply mean “related to a funeral” such as in the phrases funereal rites (ritual actions) or funereal vestments (funeral clothing).
Funereal can also be used in a more abstract way, to describe a very “dark” mood, style, or atmosphere, such as in “a funereal tone of voice.”