I've noticed that some cards say "counter target spell or creature" but turn aside only says "counter target spell ..."
No, Turn aside cannot counter Noxious Gearhulk.
There seems to be some confusion here. When a player plays a creature spell such as the Gearhulk, it is indeed a spell while it is on the stack and does fulfill one of the conditions of Turn Aside's possible targets. However, a creature spell (generally, all permanent spells except Auras) never targets anything, and is therefore never a valid target for Turn Aside. A creature spell is simply on the stack, and when it resolves, it puts the creature it represents onto the battlefield.
Only the Gearhulk's enters-the-battlefield ability can target something. It goes on the stack when the Gearhulk has resolved and entered the battlefield. However, an ability is not the same as a spell, Turn Aside can counter only spells, so Turn Aside cannot counter that ability either.
No, you cannot counter a Gearhulk with Turn Aside.
The Gearhulk is not a spell that targets anything. When it's cast, it's just a creature spell on the stack, without any targets and doing nothing special. Its ability isn't doing anything yet.
After Gearhulk resolves and enters the battlefield as a creature (too late to counter it), its "When Noxious Gearhulk enters the battlefield..." ability triggers and goes on the stack. Now there is a triggered ability on the stack that's targeting something. You'd have to cast a card like Stifle which counters that ability.