Is it just a matter of power?
Udyr demonstrated to be able to attune and become both Volibear and Ornn, that are known demigod, but he also became many other creatures, being these other animals that are not known for being Demigods (to us)
Are these normal spirits, or are they also demigods from another land?
Demigods are spirits in a way...Easily put demigods gain their strength from prayers and worship (Volibear does) and those worships help grant the demigods power to materialize. Demigods shape is in some way determined by the culture they appear in the most, so Ornn would probably look different to people who worship the craftsmanship in Shurima. Ultimately spirit- gods are spirits who, with enough power and worship, can materialize. Udyr also took the shape of the Boar demigods aswell as the Lynx I believe. My theory is that there is also a Stag demigod but that's beside the point. All these demigods are from Freljord tho again, they could potentially appear anywhere in Runeterra. Udyr is simply a spirit- walker who can take emotions and shape from beasts that surround him.
There are also spirits in the Freljord that are simply that, spirits. They probably can't materialize so they use their influence in another way.
The only Spirit I know of is the Drakalops. Apparently they are the wind Spirit since they are known for their speed and invincibility. My guess is that Spirits have powerful abilities, but not as powerful as the demigods. It is possible to tame the spirits, as seen by Kled and Skaarl, so they might be dumber than a demigod aswell.
Demigods are Freljord-specific, while spirits is a more general term. Spirits encompass a lot if different types of beings, but demigods seem to be defined by being an animal-like godly being, specifically from the Freljord.
In terms of power level, they're pretty darn powerful, probably one of the more powerful beings on Runeterra. Less than the gods of Mount Targon, but more than Yordles, Vastayan, or demons.
My guess for Udyr is that he simply shifted to animal spirits, which are less powerful than demigods.
The way I see it Demigods are simply a specific kind of spirit, just like demons are a specific kind of spirit.
The difference is that the Freljordians view them as "demi-gods" and deify them. There is no functional difference they are just spirits so powerful that they manifest as giants
