Yes it makes an enormous difference under immigration law. Entering without an inspection is a crime, albeit a misdemeanor for the first offense (second try gets bumped to a D felony if I remember correctly). The act of being in the country illegally is only considered a civil offense, which does not constitute a crime, and as such there can only be civil penalties (fines but no jail time) imposed. Consequently, overstaying a visa usually does not prevent you from adjusting your status in the US.

US actually takes this very seriously, because getting in without clearance presents a huge security risk, especially in this day and age, and they cannot really say "well, you got, and its our fault for not catching you so you're good". They kind of make this hang over your head for the rest of your life, and make legalization extremely difficult just to prevent people from attempting it.

Ironically enough, getting through customs with a fraudulent identity (someone else's passport etc.), despite it having much harsher consequences if caught, usually permits a waiver of inadmissibility if someone marries a US citizen (or even PR but that has its own hoops that one needs to jump through).