I am not a US rare electrical grid expert by any means, but..
I think I have read somewhere that 2-phase power in the US was used, very rare, in some places.
In most of the rest-of-world,...
power that is single phase is == 220V (== 240V, +/-).
No hot/neutral etc. The lines are equal.
A safety ground, not in use normally, and a brown/blue color for the power lines, most commonly, both carrying the 220V single phase.
Connectors not keyed- since you can invert the plug or swap the lines and everything works just the same.
Then, most 3-phase is 220-240V (less common/rare) or 380V (400V, same thing).
3 equal lines, plus safety ground, total 4.
Safety gnd is green/yellow, mostly, today(s).
2-phase power ? Whats that ?
Moral of story, I think.
Are you really in an area that has ever had 2-phase power ?
I would suspect its either single phase 220V or 3-phase 220, and thus...
the 3-phase would have 4 wires, and the single phase, US, might have 3 ?
I think the US 220 would then be line-hot-neutral in us terminology ?? or not ??
My first thought would be poor markings.
Since You say plant, I hear "big power" ie 25-40 kW and up, and thus I would never ever do a "smoke test".
Otoh, depending on motor, a lot of 3-phase motors can run on tiny current no-load.
Like 0.1 kW, or 100W, or 50 watts.
If you have a fast gfi, and a spare line, it might be possible to test it, cheaply.
Please dont do this from the main panel of a big industrial plant ..
you probably don´t want to trip the whole plant supply by surprise, when running industrial processes.
Likely (depending) to cost more than a new 40kW motor...
Grin
Interesting Question, for sure.
You did not mention power levels or data, or data from plant, but castings or transporters or process-lines generally don´t like the power shutting off unexpectedly.
Whats your goal and budget ?
If you just wanna get it running, a cheap rented 1-day genset, and try it, might be best or good enough, depending on power levels.
Ie if its a 1MW thingy, that might change things.
If it´s not-usable as-is, often it´s more trouble than it´s worth to fix it, unless someone already knows how and has done so umpteen times.
In my old biz, the top techs were very good, and would connect a 50 kW line, hot, into machines.
Note hot.
Line by line, all 4, while energised.
I would never, ever, do that, myself.
Just not brave enough.