The concern is correct, since just passing the VGS threshold will not give the MOSFET its full current capability. Also, please refrain to say "open the MOSFET" since it's not clear: in hydraulics open valves pass fluid, in electronics an open MOSFET stops the current. It's better to say "put in conduction". And stay away from the "saturation" word used for BJTs since FETs use it for another thing.
That said, there are MOSFET specified for a gate drive as low as 1.8V, last time I checked. Your FDS is a "logic level" MOSFET, while the PSM is a "standard level" MOSFET. Aside from the name you can see the type looking at the voltages the RDSon is specified:
- Standard level have it specified at 10V, and are usually driven at 12V
- Logic level have it specified at 4.5V and are usually driven at 5V
Logic level MOSFETs often have both specified since usually they can handle more current when driven at an higher gate voltage (this is a rule for MOSFET: more gate, more current, until it breaks the oxide!)
Also, depending on the PWM frequency you'll have some non-trivial current floating into the gate: at each cycle the gate is charged and discharged since it is, in fact, a capacitor. The relevant info are in the gate charge section of the datasheet and are useful to compute switching losses (but that's a slightly more advanced topic).
In the meantime I suggest you to use a dedicated gate driver IC. You can actually do one with just two transistor but if you can use an IC is easier and more reliable. Almost every IC maker in the world makes them. If you have 12V available from the supply just use it to power the driver and use either MOSFET. Otherwise you'll need to find a 5V supply somewhere and use a driver rated for 5V operation (and you can't use your PSM part)