A firm has a monopoly whenever it has enough of the market that it can control prices in that market or exclude competition. To have a monopoly, a firm does not have to actually use that power. Having a monopoly is not illegal.
Monopolization is illegal. In order to be guilty of this, a firm must first have a monopoly. But then, it must also have gotten that monopoly or be trying to maintain that monopoly through illegitimate means. In other words, in order for a firm to be guilty of monopolization, it has to be engaging in conduct that tends to destroy competition and hurt consumers.
Thus, holding a monopoly can be seen as a passive state that is not illegal while monopolization is active cheating that is illegal.