What's the difference between gegen and wider?

Question

Answer

"Wider" is quite old-fashioned. You will hardly find it in modern texts or conversations, except a few fixed expressions like "wider den tierischen Ernst" or as a part of verbs like "widersprechen", "widerlegen" etc. 
For your active vocabulary, it will be enough to use "gegen".

Answer

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.

Answer

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