The only exception is when the hand grenades are replaced by the XM148 grenade launcher on a CAR-15. They act as they do in Battlefield 1942. The Americans and South Vietnamese use the Mk. II whilst the North Vietnamese and Viet Cong use the Type 67 (a Chinese copy of the M24 Stielhandgranate). Each Kit with hand grenades carries a maximum of 4 grenades.
In Battlefield Vietnam's WWII mod, Grenades are issued to the Assault, Heavy Assault, Scout and Flamethrower kits. They have the same stats and performance from the base game, and use the same models; the NVA grenades are used by the Imperial Japanese Army, whilst the American grenades are used by the US Marines.
Because Battlefield Vietnam features different loadouts for each faction, this list may not be specific enough. Please see each faction's respective page for information on individual weapon kits and loadouts.