Moving Multiple appended objects behave different with Move tool and Grab. After appended the objects (collection in this case), some of objects move would move in other axis independently when drag a specific axis gizmo of the Move tool. This problem doesn’t occur when using grab shortcut g + x (move in x axis). What’s the difference between to the two tools?
Possibly you had local axis selected rather than global? or individual origins? So if the objects were rotated off-global, they may follow different path if moving say on the ‘x’ axis.
Yes, they’re on local axis with individual origins and probably rotated off global. But why the two tools behave different? I had impression Move tool and grab are the same thing.
When move tool is selected there appears to be a separate option for orientation.
So one works when you move it with tool and another with g+axis 
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