Wallets and Accounts
There are two ways of "owning" Bitcoin. Wallets or Accounts.
Wallets are the way originally intended by the creator of Bitcoin. They allow one person to pay money to a second person without the need for any third party such as Coinbase.
Accounts are a way in which businesses exploit Bitcoin to make profits from it. They offer people an alternative way of "owning" bitcoin (actually just IOUs for bitcoin) and they sometimes call their accounts wallets. Somewhere in the background there is a part of their system that interacts with the Bitcoin network where necessary. Note that the main reason Bitcoin was created was to avoid any need for using (and trusting) businesses such as Coinbase.
What is needed is an electronic payment system based on cryptographic proof instead of trust,
allowing any two willing parties to transact directly with each other without the need for a trusted
third party.
- Bitcoin: A Peer-to-Peer Electronic Cash System, Satoshi Nakamoto, 2008 (my emphasis)
Addresses
Early Bitcoin wallets allowed you to create new addresses, but many people didn't use that feature and only used one address. So people often thought of that address as a wallet address. In reality their wallet could have as many addresses as they want.
A modern Bitcoin wallet is a type called a Hierarchical Deterministic (HD) wallet which usually generates many addresses automatically and generates a new address every time you use it to request or create a payment.
So, for privacy reasons, you should use a new address for each transaction and should think of each addresses as an address for a specific transaction rather than as an address for a person's wallet.
Addresses starting with 3
normally indicate a type of Bitcoin script called Pay to Script Hash (P2SH). These addresses are around 34 characters long - the ones in your image look shortened. Someone sending money needs the full address. Since your screenshot labels these as assets, they are likely addresses that have already been used to receive money. You should be able to re-use these addresses (unless Coinbase do something strange) but there should be a clear option elsewhere to generate a new address, perhaps labelled something like "receive payment" or "create invoice" or some such phrase. Coinbase should have some support contact who can assist.
Addresses in the Bitcoin Network
Some unintiutive facts about addresses:
- Unlike postal addresses, a Bitcoin address does not identify a person or a place.
- A Bitcoin address is actually just a way for a payee to pass enough information to a payer for that payer's wallet to create a Bitcoin locking script in an output of a Bitcoin transaction.
- There are no Bitcoin addresses transmitted or used in the Bitcoin network protocol. Only locking and unlocking scripts.
It has been suggested that a phrase like "invoice reference" might have been a better name than "address". However it is probably too late to rename it.