It helps to pick some numbers.
Suppose your billing periods are all from the 10th of each month to the 9th of the next month (e.g. 10th August to 9th September).
Between 10th August and 9th September, you can pay into the account as many times as you like, and you can withdraw from the account as many times as you like (subject to credit limits, etc). Say you started with a clean slate on 10th August, and over period from 10th August to 9th September deposited a total of $500 and withdrew a total of $600.
The bank works out the balance on 9th September:
- starting $0 - amount paid in $500 + credit drawn $600 = net $100 credit used
You now owe the bank $100. This is the principal on which interest would be calculated, subject to interest-free periods, late-payment penalties etc.
In your examples:
I receive a statement: Balance of $500 on my card. I pay off in full, before the due date. Then I accrue another $500 before the due date. Come due date, am I charged interest?
- start $500 - paid in $500 + credit drawn $0 = $0
Principal = $0, so there's no interest expected to be paid.
I receive a statement: Balance of $500 on my card. I pay off $200, then accrue another $200 before the due date. Come the due date, am I charged interest on the full $500? $300? Other?
- start $500 - paid in $200 + credit drawn $200 = $500
Principal = $500, so expect to pay interest on $500. Now, there are probably rules about interest-free periods that take into account the dates of individual transactions, so it's not just a straightforward 'interest rate x principal' calculation. The start $500 - paid in $200 amount ($300) is likely to be accruing interest all the way; the credit drawn $200 might also be accruing interest because you didn't pay in full the previous month. And if you didn't pay in time the month before that, there might be yet more charges.
I receive a statement: Balance of $500 on my card. I pay off $200, then accrue $300 more. At due date, what portion of the $600 is subject to interest?
- start $500 - paid in $200 + credit drawn $300 = $600
Principal = $600, with comments along the same lines as the $500 principal example above.