Do people ever get a seizure without convulsions?

Seizures: Yes, there are many types of seizures and not all have convulsions as part of their presentation. It depends on the part of the brain which the seizures is affectinf. Absence seizures, sensory seizures, visual seizures, etc, don't have convulsions in association, unless it spreads to other parts of the brain.

Yes: Convulsion is usually to describe a seizure with loss of consciousness and jerking of the arms and legs. There are several types of seizures that can occur without the symptoms of convulsion. For example partial seizures, some primary generalized seizures, seizures that represent sensory features or forced thoughts.