It depends. Outlets are manufactured so that both sockets are powered from a single source - one hot wire and one neutral wire and a ground wire for safety.
On almost all outlets, those sockets are connected by small tabs of brass that feeds the connections from one socket to the other. If you attach the hot and neutral wires to the screws for one socket, these brass tabs carry that connection to the other socket. It works the same way if you use the press in connections which are holes on the back of some outlets (but many pros and DIYers do not favor using press in connections). The brass tabs on the side carry the power from one socket to the other.
You can change this. If you break off the brass tab on the hot side, the hot wire you attach to one socket does NOT carry over to the other socket within the outlet. This technique is often used to have an outlet with an always live socket (for clocks, etc,) and a switched outlet (for bedside lamps). The outlet is wired with two separate hot leads, one that is always hot and one that goes through a switch. They could be on the same or different breakers depending on several factors. The neutral side may or may not be connected depending on several factors that are not critical here.
You can also separate the sockets if you wanted a dedicated socket for a high draw device, such as a heater, and run a separate line from the panel. (This generally would require a separate neutral).
In your example, if the sockets are set up conventionally, that is powered from a single line, there is no difference, except plugging into a socket is a marginally safer approach than multiple splitters. Be sure that the overall load that is likely to be used at one time does not exceed the capacity of the surge protectors or the circuit breaker on the line.
Any equipment that uses a two prong plug will be as safe being plugged into this setup as they would be if they were plugged into a properly grounded three prong outlet. Two prong plugs (obviously) do not use the ground pin. As for three prong plugs, this depends on what is being plugged in. If the item is a laptop power supply that is sealed in a plastic shell, the ground pin is pretty much ISO-proforma [meaning, that is the standard cord- whether the equipment needs a ground or not.] I would be hesitant to plug in something with a metal shell, like a full size desk top tower, because the power supply is enclosed in a metal shell and attached directly to the frame of the case, this could present a shock hazard if the power supply were to malfunction.
A GFCI is a good start. If they are functioning properly, they will guard against lethal shocks, but you may still get a tingle if the electric is not quite right.
A possible suggestion: Use a 2->3 pin converter and attach a ground wire to the grounding tab. Attach the other end of the wire to a radiator if you have steam heat or possibly a metal water pipe. (no gas pipes.) This will get you a ground and you can use those items safely.
Best Answer
The surge protector will dump high voltage spikes from hot to the ground and many will drop from hot to neutral, so it would depend on the model, if internally the mov’s or metal oxide varistors are wired hot to neutral you would still have spike protection. If only wired got to ground it will do no good as their is no connection.