Does any wabble from a wheel indicate that its out of true? Or could it possibly be something else?

Possibly something else, yes - but generally the definition of out of true is that the wheel wobbles. If the bearing is too loosely adjusted then the wheel could also wobble, but if it always has the same back and forth pattern when turning the rim/true is the issue.

Bear in mind that simple truing (spoke adjustment) may not always correct an out of true condition. If the rim has been physically bent by impact just adjusting spokes will not correct it. If you get the rim straight but some spokes are much looser than others the rim is physically bent. I generally advise anyone who is showing little experience with wheel structure and truing to have a bike shop or experienced person tackle a bent rim.

And sometimes you'll get a wobble feel under load but it spins beautifully straight on a truing stand. That means you have a straight rim but very loose spokes. You should check for even tension. No spokes should be really loose. If you're not experienced enough to know how tight they should feel, ask an expert.

Wheel wobbles because the spokes have been stretched and the wheel is out of true; a broken spoke; a bent rim; a broken axle if it has an axle; a bent hollow hub guide, the part that the skewer goes through, possibly a misaligned dropout guide, the groove on each side that the wheel slips into, maybe this is bent and not aligned.