Shortage in the absence of price controls generally means that something is inhibiting supply from increasing as demand does, causing increased demand to have the primary result of increasing prices rather than increasing production.
Sometimes this is expected or unavoidable, e.g. if you have a sudden increase in the demand for electricity then the price will increase temporarily until new power generation or transmission capacity can be brought online, and in the meantime you have a shortage.
The problem comes when the shortage is a result of artificial scarcity as it is with housing/zoning, because then it's not temporary, it persists until the cause of the artificial scarcity is defeated.
Shortage is almost always used with a hidden assumption that the current price is "bad."
Truckers are currently retiring faster than they're being replaced. So some folks are saying there's going to be a "trucker shortage." In reality, there are plenty of people out there who could get a CDL license and drive a truck, but don't. Why? Because the compensation for being a trucker isn't high enough because the demand isn't high enough.
For housing, from the house seller's point of view, they could have the viewpoint that there are far too many houses for sale, the supply is too high, they want a higher price for their house. And from the buyer's point of view, there aren't enough houses because they want to pay a lower price.
I'm not saying either side is right/wrong or good/bad. It's just that "shortage" isn't a very useful word.