Safari and Mobile Safari are common and are neither Firefox nor Chrome derivatives.
Uncommon and neither Firefox nor Chrome Derivatives: Netsurf, Dillo, Ladybird each have their own engines. A few browsers also use a Gecko fork called Goanna. (Pale Moon comes to mind first, but there are at least a couple others that use the same engine.) Then there's Konqueror. It's not common, but can either use old KHTML or WebKit (Safari's engine).
Uncommon and neither Firefox nor Chrome Derivatives: Netsurf, Dillo, Ladybird each have their own engines. A few browsers also use a Gecko fork called Goanna. (Pale Moon comes to mind first, but there are at least a couple others that use the same engine.) Then there's Konqueror. It's not common, but can either use old KHTML or WebKit (Safari's engine).