Yes. (I mean, you may even get more. But the important point is that in the first case you do not have a deposit and the bank doesn't owe you anything.)

with some caveats: if you keep $250k in your personal checking, another $250k in your personal savings, another $250K in a joint checking account, another $250K in a joint savings account, all accounts being with SVB, you will get $1M back. FDIC states "The standard insurance amount is $250,000 per depositor, per insured bank, for each account ownership category"