I would imagine that standard of crypto is similar: public address / private key / signing transactions...
Not only can there be variation in the hash functions and methods used for converting private keys to public addresses... there are also different methods involved in signing transactions... look at the differences between Bitcoin and Bitcoin Cash that were implemented to prevent "replay attacks"... and again with Bitcoin Gold... they added their own little twist as well.
The fact that there are multi currency wallets (Coinomi, Jaxx, Exodus etc) is actually pretty impressive. I doubt there will ever be "One Wallet To Rule Them All"™