Razorback Transport
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 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.
Overview
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 (which don't exist any more anyway), 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 (because that's what it is). 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.
Patterns
There is a few noticeable patterns for the Razorback, these are:
Infernum Pattern Razorback
One of the first known patterns of Razorbacks first seen in the release of Imperial Armour Volume Two - Second Edition. The Infernum Pattern Razorback is an interesting-looking pattern found nowhere else.
According to the fluff, it is believed that Techmarines of the Fire Hawks Chapter formulated a means of overcoming the power feed issue and first used the new vehicle variant during the Badab War, where this advanced type of Razorback was used to smash through enemy fortifications and deliver squads directly through the breach with its Multi-Melta. The New variant was named Infernum Pattern Razorback, and how the Fire Hawks avoided twisting the AdMech's panties over such unsanctioned modifications, we have no idea.
In terms of its looks, the Infernum differs from the normal vanilla due to its unique and more advanced-looking turret. Whereas the normal Razorback just has a remote-controlled turret with a small camera attached to it, the Infernum variety has a suite of advanced thermal and camera systems; akin to that of a Tarantula Sentry Gun turret. This probably gifts the Infernum better accuracy and stability over nighttime operations and heavily obscured environments. Currently, the only known weapons is the aforementioned Multi-Melta, although we wouldn't be surprised if it is capable of also carrying the other stock-standard Razorback armaments.
Rikarius Pattern Razorback
The Rikarius Pattern Razorback or simply known as the Razorback Rikarius is a pretty unique pattern as it is another example of community friendliness; where a one man's conversion was given house rules by GW and completely canonised as can be seen here:
Fluffwise, the Razorback Rikarius is a Razorback variant used by the Blood Ravens and others. It was first developed in M37, when a resurgence of Ork forces in the Aurelian System prompted commanders to produce a tank that could eliminate vast amounts of infantry. The resulting vehicle was named after Yriel Rikarius, the Blood Ravens 2nd Captain at the time who had connections to the High Magos M'Lell of Mars.
M'Lell ensured the revised Razorback STC was quickly fabricated and put into service alongside the embattled Blood Ravens. Sacrificing transport capacity to mount a variety of weapons such as twin-linked Assault Cannons and two Hurricane Bolters, squadrons of these vehicles have since served many other Space Marine Chapters. Ergo, treat this as the Razorback's equivalent of the Land Raider Ares, where it really puts the Infantry Fighting in infantry fighting vehicle. In the intervening centuries, their numbers have dwindled and the STC lost, which has resulted in the surviving vehicles being treated as relics.
Crunchwise, it is a more expensive version of the regular Razorback due to sacrificing its remaining troop transport capacity with MOAR GUNS. Suffice to say, this thing is a monstrous TEQ sweeper that eats hordes for breakfast. Considered as the primary tarpit breaker for Space Marines for such a compact size. Although it is more expensive for an already costly vehicle, but when facing against Tyranid and Ork players, the value in deleting hordes should be worth the cost.
Vortimer Pattern Razorback
Basically, the Land Raider Vortimer Redeemer's little brother.
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 armoury, meaning that every deployment of these venerable vehicles must be approved beforehand by the chapter council.
These vehicles were personally constructed by Master Armourer Regis Vortimer himself and were for the Deliverance of Vulgate.
On 8th Edition tabletop, this is a Razorback armed with the aforementioned twin psycannons, which in practice is effectively the same as the Assault Cannon variant, albeit with 4 fewer shots and +1 Strength. Nowhere near as flexible as the vanilla Razorback, but we still have access to those anyway. Thanks to Chapter Approved increasing the points cost on the twin psycannon by more than three-quarters of its original cost, this is really not worth considering anymore. For fuck's sake, the gun now costs two-thirds of a Rhino.