The driver technically is under arrest because the driver is not free to leave until the officer has written a ticket (or if it’s the driver’s lucky day, only issued a warning). But the arrest is temporary.

Detention vs. Arrest: Although issuing a traffic citation is technically an arrest and release on the person's written promise to appear, it is treated as a detention because of the minimal intrusion involved. (Berkemer v. McCarty (1984) 468 U.S. 420, 439 [82 L.Ed.2nd 317, 334]; see also People v. Hernandez (2006) 146 Cal.App.4th 773: "Traffic stops are treated as investigatory detentions for which the officer must be able to point to specific and articulable facts justifying the suspicion that a crime is being committed.")