It is, yes, and ultimately says the same thing. I prefer the alternative phrasing as I think it more clearly explains the mechanisms, especially when people sometimes confuse demand to mean 'I want something'.

> Capped prices is one potential cause, but demand also isn't always very elastic and this can cause shortages on it's own.

I don't see it being contradictory. In an ideal model of inelastic demand, the demand never wanes no matter how high the price goes. However, price cannot continue to rise infinitely, so you have technically created a situation where price cannot rise again. It is still the price not being able to rise that characterizes the shortage in this case.

I did not mean to suggest that the government is the only thing that can cause prices to stop increasing. It was just one example.