I know equipment is koed when a character changes zones. But what are zones? I thought equipment followed a character (IE: if a player is returned to your hand, the equipment also goes to your hand). Or...if you steal a character with satanus, the equipment would follow to your side of the board with the character. Is this correct?

The second example I think it is, the first one I'm pretty sure isn't, if ia character is returned to hand it loses the equip. Also by zones it refers to visible and hidden, if i move my character in between them, the equipment gets KO'ed

Moving between the Hidden and Visible is not changing zones, it is just changing areas. Equipment is KO'd by this movement because of a different game rule.

Zones include the Hand Zone (your hand), the Deck Zone (your deck), the In Play Zone (front, support, resource), etc. Moving a character from the In Play zone to another one will cause the equipment to fall off because the character changed zones. If a character is returned to your hand, for example, the equipment will be sent to the KO pile.

Moving between the hidden and visible areas will cause the equipment to fall off because of the rule about changing areas, but is easier to subvert with card rules (see Medallion of Power).

Taking control of a character with Satanus is not changing zones (you stay in the In-Play zone), so the equipment will not fall off. However, taking control of a character with In the Hands of Qward may cause equipment to fall off if you take control of a visible character with it (as the effect moves the character to the hidden area).