Are they or aren't they?

"Yes, crossing the U.S. border unlawfully is a federal offense, though simple undocumented presence (such as overstaying a legal visa) is a civil violation.

Distinction Between Entry and Presence

• Illegal Entry (Misdemeanor): Under 8 U.S.C. § 1325, entering or attempting to enter the United States at any time or place not designated by immigration officers, or eluding inspection, is a federal misdemeanor. A first offense carries a penalty of a fine, up to six months in prison, or both.
• Illegal Re-Entry (Felony): Under 8 U.S.C. § 1326, unlawfully re-entering or being found in the U.S. after a prior deportation or formal removal is a felony. Penalties range up to 2 years in prison normally, or up to 10 to 20 years if the person has prior criminal convictions.
• Unlawful Presence (Civil Violation): Being present in the United States without legal status—such as individuals who entered legally on a visa and subsequently overstayed—is a civil infraction handled through immigration (deportation) proceedings rather than a criminal charge."

Meme courtesy of Musicman.