Are intra state and out of state ONLINE savings/checking/CDs/money market accounts FDIC insured same as local brick & mortar bank accounts?
Usually they are, but of course you should check the registration number the bank shows against the FDIC website to make sure you don't fall for a fake.
In case the account is offered by a credit union rather than a bank, they will have insurance through NCUA instead of FDIC, verify NCUA charters here. This applies to both online and brick-and-mortar credit unions.
Money market accounts in particular may be provided by yet another type of financial firm: a brokerage. Those are insured through SIPC and there are significant differences in what protection is provided vs FDIC and NCUA insurances. Note that many brokerages provide a "sweep" service, such that when not actively involved in a trading transaction, money is actually held in a bank account where FDIC applies. The particular broker should be able to tell you which bank holds the sweep accounts.