Street Legal Race Cars
"Race car" covers a lot ground. Lots of race cars would be street legal, and you can race just about any street-legal vehicle.
As already pointed out, there are equipment requirements for street legal vehicles such as lights, turn signals, horn, mirrors, etc. In the U.S., at least, there are other requirements, some well-known, such as emission thresholds, some less well-known, such as minimum height of bumpers, size and shape and position of bumpers, etc. It's not far-fetched that some cars in some racing classes meet all such requirements and can be insured and registered for street use.
The converse can also be true: many people race their street vehicle, for example, in the U.S., in SCCA Solo I (more commonly known as time trial) and Solo II (more commonly known as autocross), Rallycross, in NHRA drag races. I raced autocross for ten years. I would drive my street vehicle to the event, change to race tires, race, put street tires back on, then drive home i.e. I drive my "race car" on the street.