If you look at the German dictionary Duden or other dictionaries you will see that especially 'gegen' has many meanings (https://www.duden.de/rechtschreibung/gegen_zu_wider_an) 'Wider' is either a prefix to verbs or a preposition (https://www.duden.de/suchen/dudenonline/wider), so it would help if you could narrow down your question.

'gegen' can be understood as versus, wider is more like 'against'. as always, context is needed for more precise semantics.