No. Knights were a particular section of the nobility, below the level of lord but above that of esquire. Indeed, one could argue that they were the foundational element of the nobility, since fiefdoms were made up of knight’s fees.
They paid for their armor usually in cash from the feudal taxes and rents that they extracted from their knight’s fee.
And knights usually did “own” land – the aforesaid knight’s fee – although there were household knights or tourney knights or the like.