What's the difference?
What are definitions?
Well, from what I can tell, saying a transformation of a system is isothermal indicates no net change in the internal energy of the system, implying [itex]\Delta U = 0[/itex], implying [itex]W = -\Delta Q[/itex]. Adiabatic changes only entail no heat being added or subtracted to or from the system. So there isn't necessarily a zero change in U, since the system can do work, or have work done on it.
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