The military records you describe don't sound at all unusual. Apparently Mr. Ash had a physical condition or some other qualification (age, occupation &c) which provided an exemption from Confederate military service. The State of Texas had a different set of rules for militia service, but the very fact that Ash was NOT in Confederate service made him a candidate who might be called. If he had returned to Confederate service, you could call that a reenlistment. Since this was the first time he was called into militia service by the State of Texas, it's simply an enlistment.