Input Phase Angle and number of transformers needed. For High-Delta, type of transformer.
All voltages below are expressed in RMS Average, not Peak...
I find it really hard to refer to Split-Phase as Residential or "House" Power. It is used in business where you're not running a lot of heavy motorized equipment. 240VAC Split Phase is produced off a single phase input transformer with center tapped secondary, producing for output, a single phase across the 240V outer terminals and two 120V legs with phases 180 degrees apart. Centertap is an effective ground (Neutral) at 0V potential and each leg is +120VAC and -120VAC respectively for the full voltage of 240V.
If you view the waveform on an oscilloscope, you will see a single sine wave (single phase) when measuring between Line 1 and Line 2 (below) at 240VAC RMS. Measuring between Line 1 and Neutral will show a single sine wave at 120VAC RMS, measuring between Line 2 and Neutral will show a single sine wave at 120VAC RMS equal and opposite to the L1-Neutral wave (180 degree phase shift)
Three Phase has three separate circuits with phases 120 Degrees apart. You need three separate transformers, one for each phase. The primary on each is fed with a single phase and produces an output of a single phase on 208 (Y) or 240 (Delta) VAC. Depending on whether the circuit is Wye or Delta, you can have multiple voltages. Each phase-pair carries the full voltage. On Wye with Neutral, the voltage between the phase and Neutral will be slightly less than three-fifths of (it's one-third of the square root of 3, for electronics geeks) the voltage between each phase leg. On Delta, you only have each phase available with no Neutral.
If we hook up an oscilloscope to each of the line terminals, we see the following waveform, three independent power paths, 120 degrees phase shifted which when applied to a three phase motor, provide a rotating vortex magnetic field which makes 3 phase motors self-starting without the requirement of a start capacitor, start winding or other method of kludging in a phase shifted winding to provide the rotational force to start the motor spinning.
Wye and Delta typically have one Pole Pig per phase (three transformers). On a Wye 480VAC system, the voltage between each phase and Neutral is 277VAC. Transformer secondary electrical schematics below to show how each transformer set is hooked up to derive the connection scheme. You can hook a single phase motor up on L1-L2, L2-L3 or L3-L1 for single phase current (balance necessary on loading between phases) or apply L1-L2-L3 to the proper therminals of a three phase motor.
On the US power grid, also is used the High-Leg Delta transformer circuit which allows for multiple voltages. Voltage between each Leg produces 240VAC, voltage between the Center Tap and the high leg gives 208VAC Single Phase and voltage between each low leg and the center tap is essentially a Split Phase circuit with 120V from each respective leg to Neutral (residential power tap - grin). High-Leg Delta power is only available in 120/208/240, and is not put in any longer as Wye circuits are preferred instead for their relative simplicity and improved load balancing
If you're not using the neutral, you should have a NEMA 6-30 receptacle instead of a NEMA 14-30.
Other than that, it looks like you're all set. The black wire is one line (L1), the red wire is another line (L2), and green is ground. You should have 240 volts between L1 and L2, since you have a 120/240V single split-phase system.
You don't have to worry about the three phase warnings, since you don't have a three phase system.
Best Answer
Here's what 3-phase delta looks like.
This happens to be 240V and uses the common 3-phase colors of black, red, blue.
It's that simple, folks. 3 phases, No Neutral.
One error of belief is thinking every service must have a neutral. It doesn't. This was Tesla's genius.
Delta is used in industrial facilities where a few tools need a medium amount of power for a few larger tools. It would be rare to see lighting or other minor loads run off it. A motor which takes 240V 3-phase can typically be jumpered to also work on 480V 3-phase, and that is much more efficient to distribute. I would never install 240V today, I'd install 480V.
Obviously there's only one voltage. Pretty straightforward. Now what's this?
It's the exact same thing. The only difference is using alternate colors. The point here is that any color may be used (except white, gray or green) including orange. NEC doctrine is the electrician is expected to measure the circuit to determine voltages. Prince fan? Use Purple Pink Black.
Hook your heater between any two hots.
They are all 240V. Done.
The only other issue is balancing. If you have several loads, try to put them on alternate phases so you load the 3 phases evenly.
We're done here.
So what's this Other Thing then?
This thread is dominated by discussion of some other system which is not relevant to OP. It's a red herring. But since it keeps coming up, let's talk about it. This is "high-leg" or "wild-leg" delta, which is a clever rearrangement of delta to get 120V single-phase loads also - to avoid the cost of a separate 240/120V single-phase service. See how a neutral has been added halfway down a phase.
If you want to use 120V appliances, this only works on 240V delta.
Notice two mandatory wire colors. Of course, neutral must be white or gray. The "wild leg" - with much higher voltage to neutral - must be orange. It's one of very few cases where a "hot" color is mandated. However in any other circuit, you can use orange for any hot, and that's exactly what happened in our second example. That means if you see black-red-orange-white, it could be anything including 600V wye. You better test it.
So when someone says "Delta" they do not mean "wild-leg delta". They mean "delta". Don't go buying something that needs 120V or 208V expecting it to be there in delta service. It won't be unless they specify wild-leg/high-leg.
All the 120V loads load up the A-C phase. If there's a desire to run a significant number of 120V circuits, 208V "wye" 3-phase does a better job of it, while allowing loads to be balanced. If lighting is the primary load, 480V "wye" is a "swiss army" voltage, allowing 240V/480V motors to run in delta connection and lighting to work in wye, using a hot-neutral 277V connection.