What is the difference between using the receive payment function verses creating an invoice/pledge when you deposit a check?

A pledge(invoice) increases an Income account on the one side and increases Accounts Receivable on the other - it is not a bank transaction.  A Receive Payment receives money into the bank account for a previously created Pledge, and reduces Accounts Receivable.   You can combine these two actions into one with a "Sales Receipt", which increases an Income account and puts the money directly in the bank, bypassing Accounts Receivable.  

Note that if you have multiple receipts in one bank deposit, you should put the money into "Undeposited Funds" (instead of the Bank account), and then do a Bank Deposit from Undeposited Funds (which QBO tracks for you - in the top section of the Deposit form). This way the line items in the bank register will match the bank statement,making for easier reconciling.