Fare un giro...
My understanding of “fare un giro” is to go for a walk, to go around, to do a tour.
Also, eg “fare un giro al centro commerciale” it means to walk around the shopping center.
How about “andare in giro”? Are they the same?
Andare in giro = To wander, to walk without a fixed destination.
Fare un giro = To go for a walk (or a ride) / to go on a tour.
They are not the same (albeit they are similar), but in some contexts you may use either of the two:
Siamo andati in giro in centro. = We went walking in the city centre / downtown.
Siamo andati a fare un giro in centro. = We went for a walk in the city centre/ downtown.