The parallax is intended to be a criterium bike with tighter geo than the vigorelli.
The vigorelli is intended to be an all-around track bike.
The MASH frame aka the Bolt, histogram, OG grays green/white (same frameset/ geo but with different MASH livery) is a tamer pursuit frame that makes it streetable/ bearable to ride.

Technically any track bike is also a streetbike. All of the above are originally supplied with forks that are pre-drilled by Cinelli but cosmetically hidden behind a cap. It's right behind the bulls-eye fork motif on some models.