No problem.

Two hots for the 240v.
One hot& one neutral for the 120v.
One ground for the whole conduit.
The ground must must be sized according to the largest circuit in the conduit.

I need further splainin'
Black and red from the hots in the 220 outlet to the 220 breaker.
Green from the neutral in the 220 outlet to the ground bar in the breaker box.
White from the ground bar in the breaker box to the 110 outlet.
Purple or some other color from the 110 breaker to the 110 outlet.
Short green wire from 110 outlet grounded to metal conduit.
Is that all correct?

Green does NOT go to the neutral. It goes to the GROUND. If you need a neutral then you must use white.
You could use black or red for the 110 also. Just number the ends of the wire so know which is which at the other end. Purple is fine to use also.

I assume your wire sizes are AWG 6 or smaller. In such a case you have fewer options regarding insulation color.

The neutral (on the 120 volt circuit) must have a white or gray color over its entire length. The white or gray color may only be used for a neutral. NEC 200.6(A)

The green colored wire must, of course, be used for grounding purposes, only.

For the hot wires, the NEC does not specify the colors for the circumstances you have. However, your local AHJ may specify them.

If I were wiring up 2 circuits like this with a single cable assembly (NM/Romex, for example), I would get the cable that would normally be used for three phase circuits, which has 3 hot wires with black, red, and blue coloring (not normally stocked an home improvement stores ... you'll need to visit a real electrical supply distributor to find it). In conduit, I'd use those same colors as singles. I would also pair the black wire with the white wire to the 120 volt outlet, and pair the red wire with the blue wire for the 240 volt outlet.

But ask your local AHJ (the electrical inspection office) for a copy of local rules that may apply.

I am assuming your 240 volt outlet is a single voltage (NEMA designation 6-XX), as opposed to a dual voltage 120/240 (that you usually see for kitchen stoves and laundry driers). If you have a dual voltage outlet, you also need a separate neutral wire for that (I'd try to find gray wire if running it in a conduit).

The 220 volt outlet will be for a jointer which pulls I believe 13 amps max, so I was just going to use 12 gauge wire. No 110 coming off of it.
So if I use black and white for the 110, and red and blue for the hots on the 220, what do I use for the ground or neutral on the 220?
Perhaps I'm confusing you and me by using the phrase "neutral" for the wire from the ground bar in the breaker box to the non-hot connection in the 220 outlet.

The "non-hot" connection is not a neutral. It is a ground. You do not separate the grounds, just run one green for the 220 and the 110 receptacle. Black and White for the 110 and red and blue for the 220, and one green ground that you also connect to the metal conduit, etc.

And 220V doesn't use a neutral.

So the green wire goes from the ground bar in the circuit box to the a junction point where the two circuits split off from each other. There it splits, one green wire going to the 220 outlet, another going to the green screw post on the outlet, also connected to the conduit?

The 240V circuit does not use a neutral. It is the 2 opposite ends of the split 120/240 volt electrical system, only. Either of these hot wires would be 120V relative to neutral, but that's not what this circuit is about. Typical home appliances that use a 240V (only) circuit include electric hot water heater and heady duty air conditioners.

The split voltage circuits that do use a neutral in addition to the 2 hots do this as a way to have 2 voltages at the same time. A Clothes dryer uses this to run the motor on 120V and the heating elements on 240V, so they can use a common motor for the gas version of the dryer. A few do use a 240V motor and technically don't need the neutral, but having the NEMA 14-30R outlet for a dryer, and using the matching plug, is just a common standard these days. Older electric stoves use the 240V for heating elements and 120V for the clock on the panel so they can use cheap clock motors, as well as the convenience outlet that stoves used to have. Some modern stoves run everything on 240V since they are digital these days and switching power supplies to drive them can be cheaply made to run on 240V.

Almost all heavy duty shop tools that need more than 120V will use 240V straight (no neutral used), if they don't use three phase.

The green wire needs to be joined at the junction in such a way that it does not use the junction box frame itself as part of the path it takes to the outlets. So that would mean 4 green green wires under one wire cap (1: from the panel, 2: to outlet 1, 3: to outlet 2, and 4: to the junction box itself).

In the breaker panel, you should tie the black and white wires together (not too tight, just enough to "leave a message" indicating they go together), and tie the red and blue wires together. The red and blue, of course, go to a 2-pole breaker. This is to comply with NEC 210.4(D).

So the green wire goes from the ground bar in the circuit box to the a junction point where the two circuits split off from each other. There it splits, one green wire going to the 220 outlet, another going to the green screw post on the outlet, also connected to the conduit?

This is correct. The green must be #12, the same size as the largest circuit it is protecting.