Grapple doesn't do damage automatically.
But as part of a successful grapple check you can do 1 of the following:
Tie (if pinned)
Move yourself and the enemy up to half your speed
Damage the enemy with a light or one-handed weapon or natural attack
Edit: Whoops, didn't realize this was a Starfinder question.
Yes you're correct, grappling doesn't offer a way to do damage in Starfinder.
Grappling was honestly too good in Pathfinder, so they weakened it considerably in Starfinder.
Thanks. Hmm I feel like that will change for monsters.
Possibly. They also might allow it as a feat in the future to allow you to deal damage with a successful grapple check, or maybe change the action economy such that you can as a full round action make a grapple check and an attack.