Gilt is the past participle of the verb to gild, so describing something covered with a thin layer of gold, or other superficial decoration:
Some walls of the Hermitage castle in St. Petersburg are covered with gilt carvings.
Gilt can also be used as a noun meaning “decoration” or “superficial beauty.”
Guilt, on the other hand, means “the feeling or condition of having done wrong, such as by breaking a law or violating a social expectation.” Guilt is a very abstract concept that we all know well. We (should) feel guilt when we do anything we consider to be morally wrong, such as lying, stealing, or hurting people. Guilty is the legal status of a person proven to have broken a law (convicted by a court of law). It is good to remember that the feeling of guilt and the legal status are quite different things.