The Razorback was developed after the Horus Heresy, and was intended to provide Space Marines with heavier fire-support. In contrast to the Rhino the Razorback loses its firing points and can only carry 6 Space Marines, but in return it gains a variety of heavy weapon options. This enhanced weapon mix means that the Razorback is a very flexible way to get more firepower on the table while still providing transport capability.
The Grey Knights are known to make use of their own unique variant of the Razorback known as the Vortimer Pattern. Armed with a set of twin-linked psycannons, only about a dozen are left in the chapter's armory, meaning that every deployment of these venerable vehicles must be approved beforehand by the chapter council.
The Chaos Space Marines were intrigued by the design of the Razorback after encountering it, but ultimately decided to simply arm their Rhinos with support weapons instead, since that didn't involve flagging down manufacturing plants (of which they don't have anywhere near as much as the loyalists) or cutting the transport capacity by 40%. As such, the Razorback remains unique to the Space Marines, aside from the occasional stolen or looted vehicle. Primaris Marines get their own flying Razorback.
Razorbacks are kind of an oddity. They have reduced transport ability (6 models compared to the 10 of a typical Rhino) and they cost a bit more (considerably more depending on the weapon option). They also lose out on firepoints, and are a much more prominent target than a regular Rhino, since their heavy weapon basically announces their threat level to everyone on the battlefield.
As such, it's best not to think of the Razorback as a tank, but rather as a light but heavily-armed Infantry Fighting Vehicle that can also carry a few troops. It is, perhaps, best-suited for use by Sternguard Veterans or Devastators, who can use the Razorback to quickly re-deploy and while adding the vehicle's firepower to their own.
Razorbacks by default come with a Twin-Linked Heavy Bolter, but they can switch this out for a Twin-Linked Heavy Flamer, a Twin-Linked Assault Cannon, a Twin-Linked Lascannon, or a combination weapon that integrates a Lascannon and a Twin-Linked Plasma Gun. Heavy Flamer Razorbacks can be useful for escorting Melta suicide squads, but the others are all better-used for supporting Devastators and the like. Tank-Busting squads benefit from a Lascannon Razorback, whereas Infantry squads often do well with just the basic Heavy Bolter Razorback. The Assault Cannon Razorback is a good compromise of power and strength. Please note that parts for the twin Heavy Flamer, twin Assault Cannon, and Lascannon/Plasmagun options are not included in the kit. However, kits for the Assault Cannon and LasPlas options can be obtained on Forgeworld.
Regardless of which you use, make sure that you're careful with them - they cost notably more than a Rhino (or Chaos Rhino w/Havoc Launcher for that matter) and you can't simply use them as expendable transports like you can with their little metal boxxy brothers - they cost too much for that. Used carefully, however, they are a godsend to any force that likes it some heavy weapons.
Model wise, it's almost always recommended to buy the Razorback box over the Rhino box, as the Razorback kit comes with everything needed to make both vehicles for very little extra money. Since the turret mounting has a different hatch from the standard Rhino, it's fully possible to build both up and use the model as a Rhino or a Razorback without any modifications (including magnetizing) to the model.
In another example of community friendliness, one man's conversion was given house rules by GW. https://www.games-workshop.com/resources/PDF/Blog/Razorback_Rikarius_ENG.pdf