People are here without documentation, or without authorization, or are overstays, or don't have lawful immigration status. Or, they may have committed even a minor infraction which renders them removable. 
People who drive while intoxicated or with a suspended license are driving illegally, but we don't refer to them as "illegals".  As a matter of fact, it could be argued that those who speed are also driving illegally.  Most people who are convicted have committed one or more illegal acts.  yet, none of them are called illegals.  We call people who who live unlawfully on someone's premises "squatters", but they are living there illegally, so why don't we call them "illegals"?  What about all of the US citizens who work off the books? Why are they not "illegals"?
If I remember correctly, a while ago, PEW published something about the fact that most of those who are here without authorization are overstays, ie they entered on valid visas.