How long does it take for an exchange to send me bitcoins? I'm not sure I understand all of the bitcoin storage options

I know there are bitcoin addresses and bitcoin wallets

what is the relationship of an address to a wallet? is a wallet mandatory and a given when talking about any bitcoin storage option?

if I had an account at a bitcoin exchange, how could I quickly move those coins from the exchange to the same wallet that I am using to dump the coins I mine?

I might not be asking the right questions, because I am not sure about the relationship between the various storage options of bitcoins (wallet, exchanges)

I would like to understand this
If you have the private key that relates to an address, then you can use that to instantly make transactions with bitcoins that are stored against that address.

However, most exchanges and online wallets provide you with a unique address without providing you with the private key for it. This is probably because they consolidate the bitcoins sent to all their addresses into a single address for the exchange, which helps them reduce transaction fees and also allows them to operate with a fractional reserve system.

In the case of a 3rd party controlling your bitcoins, you are at their mercy when it comes to the timeframe of the transaction. 

There are some online wallet services that allow you to have the private key for your bitcoins, which gives you the ability to import the private key to your own client and spend your bitcoins. In that case, you have a good level of control over your bitcoins.

The relationship between addresses and a wallet: one wallet can hold many addresses, and can even hold bitcoins against hidden addresses that have received "change" from a previous transaction.