If you have EMT, IMC or RMC metal conduit run all the way from the disconnect to the subpanel, then you can use that metal conduit itself as the grounding path, and no ground wire is needed.

Otherwise, you need to have run 4-wire cable (or 4 wires).

Sean Connery rule applies.

"There can be only one" bond between neutral and ground.

First, get your colors straight. Neutral is not ground.
Neutral = white or gray
Ground = green, yellow/green striped, or bare (that's true 'round the world).

Neutral comes from the utility. It exists in all places.

Ground is created, by you, at the very first disconnect past the meter. In that location you:

• Establish a Grounding Electrode System (grounding rods)
• Have a "ground bar" bonded to the metal frame of the disconnect
• Bond neutral to ground, in this one and only place
• Carry neutral and ground separately everywhere else.

Since neutral and ground are bonded here in the main disconnect, you can actually use the same "bar" for both neutral and ground. It's not my favorite way to do it, though. I prefer separate, isolated bars, and the fattest wire you can get as a specific neutral-ground bonding wire. The reason is, so you can put a clamp ammeter around that wire which is handy for troubleshooting a variety of problems.

As a practical thing, the meter pan itself also gets grounded because you use EMT, IMC or RMC Metal Conduit between meter pan and disconnect. Once had someone try to use PVC... they couldn't find a way to ground the meter pan. Golly!

Neural and ground are carried as separate wires

At the subpanel, place the white neutral wire on the neutral bar.

Place the green or bare ground wire on the ground bar (or rely on the metal conduit).

Any subpanel must have neutral and ground un-bonded. Can't bond it here; that would be two bonds!