Close, but not quite. 'Outside' is relative to a specified location - I can be outside your room, but not outdoors, because I am standing in the hallway.
Outdoors is outside relative to a type of location - a building. So if I am outdoors, that means I am outside of any building, in the open, under the sky.
Of course, then people start bringing pergolas and verandas into the equation, and things get messy.
So to answer your question, 'outdoors' always means under the sky, whereas 'outside', without some point or context to reference what you are outside of, doesn't.
That said, as @Catija was kind enough to highlight, in the case of the specific example sentence, most people would take 'outside' to mean 'outdoors', unless you specified somewhere else.