I only want to add if I can, that the meaning of "chez" is originally more complex, deriving from the Latin casa = house, without the subtility of the cases (declension) in modern French: "de chez" is sometimes put for "from the house of" ab casa "je vais chez..." "ad casam" "to the house of...", etc. "je suis chez moi" in casa, in my own house, i.e. home in English.
The meaning of 'chez' covers intrinsically different movements "to", "in", "into" or "from", singular or plural, according to the context of the sentence : chez eux, meaning in their house (of them : casa, casae, casam of several people) of their houses (casae, casas, casis, casarum... several houses of several people) for example in the Jacques Brel's song, chez ces gens-là...
So we can also say "son chez-soi" his own house (reflective).
Note that casa is an old Latin term meaning a little house, a little farm or a barrack instead of domus, a more formal and greater building, or villa, a greater farm, a little colony or aedes more official.
Case has more a less the same informal meaning in modern French: a little house of an indigenous in Africa, but is more formal in Spanish or Portuguese equivalent of maison in French. Casar in Spanish for exarple is to marry, 'se caser' to be married with the same meaning is colloquial in French.