I have a 750 watt SBMV bulb rated 220v and it doesn't light at all on my 120v supply. I have heard that bulbs will still usually light, but not as bright, which is fine for my intended use as the bulb is very bright. However this one won't at all turn on. I don't know if the supply is the problem and i will need a step down converter or if my adapter and cord is the problem (just using a small reptile light cord with a socket). Thanks in advance and sorry i don't know much, im not really invested into lamp collecting much.

It won't light if it's a self-ballasted mercury lamp rated at 220V, the 120V supply isn't enough to strike the arc. SBMV lamps designed for 120V are different, they have small filaments in the arc tube to act as auxiliary electrodes, whereas 220-240V lamps have the usual starting probe. You will need a step-up transformer if you don't have access to a 220-240V supply.

And if it happens to ignite the arc there, it wont warm up or will cycle, as tge arc voltage of a 230V SBMV is way too high for a 120V OCV with a , mainly with resistive ballast (the filament...). But it really depends piece by piece, or even on the exact condition and a big contribution of pure randomness... 120V is just way too low to ignite a probe start MV...

120V SBMV need electrode to be heated up before the arc may ignite (that is, what the special filaments are doing within the arctube; plus there is a thermal starter switch in the outer to control that). Neither of this is needed for 230V, there just the auxiliary probe with its resistor, like in any other normal MV, is all what the 230V mains operation need (beside the ballasting resistor filament, of course)