Will it burn it - yes.
Is "oil = oil" and it doesn't matter what you burn in it? - no.
Different 2cycle oils are formulated for different uses. For instance, my dirtbike.....I ride woods, mostly 1-2 gear singletrack (think goat trail on side of a mountain). Engine may run low to med revs. Because of this, the engine temp doesn't get very high, which means some oils don't burn efficiently, which means when running those my engine at rebuild time will have high amounts of gunk, carbon build up inside, it will run sluggish, maybe to the point of fouling plugs, smoke like a freight train and spooge out the end of the exhaust. When I run an oil made towards these conditions, the oil burns great, engine runs nice and crisp, much less smoke, no spooge out of the silencer and the engine is very clean inside come rebuild time.
Those same oils that would gunk my engine up under my normal riding conditions would be much better suited for guys racing motocross where the throttle is pinned wide open the majority of the time. Much higher revs and inside engine temps.
Both oils would protect the engine in either situation. The oils that are tailored for the conditions would do it better.
Will any 2cyl oil you pickup (or even motor oil) mix in gas and burn through your weedeater / chainsaw? Yep.
Are there better alternatives? Most definitely.
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