(covers information from several alternate timelines)
The Vulcan cruiser was a type of small starship used by the Vulcans in the 23rd century for both private and official business. Capable of landing on a planetary surface, it was common on Vulcan in the 2250s.
In 2256, a Vulcan cruiser was to ferry Sarek to a secret meeting with the Klingons on Cancri IV. However, the ship was disabled and stranded inside the Yridia Nebula by V'Latak's sabotage. (DIS: "Lethe")
In the mirror universe, Vulcan cruisers were used by Vulcan rebels fighting the Terran Empire. A cruiser attacked the USS Discovery after it entered the mirror universe, before being driven off by the ISS Cooper. (DIS: "Despite Yourself")
Used for both suborbital and interstellar transport, cruisers featured a U-shaped version of the warp ring common to Vulcan starship design. The external access hatch was located at the rear, providing access to a simple standing cockpit for two without apparent seating.
Ships of the class
Before Sarek's cruiser reveals any identifying information in "Point of Light", Burnham is quick to visually recognize the ship as Sarek's - implying there may be exterior visual differences between cruisers.
The Star Trek: Discovery The Official Starships Collection artwork identified this type of vessel as a "Vulcan Corvette" before later amending the name to Solkar-class cruiser, presumably named after Solkar, Vulcan's first ambassador to Earth  and is called the T'Pau scout ship in Star Trek Online.