Is better to use the online wallet or offline?
A offline wallet (if done correctly) is very secure, but you cant send your coins from a offline wallet without making it "online".
In short: a offline wallet never saw and will see the internet (so very secure)
online wallet: a wallet that is connected to the blockchain, so its easy to transfer money, but it's only as secure as your computer
hosted online wallet (my.electroneum.com): centralized, not (blockchain) secured, single point of failure, but if you loose your access they will able to restore it, if you loose your private keys (for a real wallet) there gone forever
I created a little overview: https://steemit.com/blockchain/@xzentorxz/different-types-of-wallets-for-blockchains