Hello and welcome to the board,
there are many different address types in Cardano and I can understand the confusion. You usually will see 2 types:
Addresses beginning with Ae2 are using the new address style that is implemented in Icarus based wallets like Yoroi and AdaLite.io (also every hardware wallet should have this type of address)
Addresses beginning with Ddz are using the older address style that for example Daedalus wallet is still using. “Older” does not mean they are bad, insecure or will stop working. These addresses are absolutely fine and they will work forever.
So to answer the most interesting question: you can send from any address type to any other and if you trust the exchange, then you should trust the wallet address it uses.
If you want to search for a certain address or check if an address is valid you can use: https://adascan.net/
If you want to learn more about different wallet types check out https://www.adatainment.com/index.php?page=cardano_wallets