Texas TRS contribution and SS question

I contribute to the Texas Teacher's Retirement System (TRS) and have a question regarding deductions for my annual contribution. 

 

Prior posts state that you cannot deduct the monthly contributions because they are pre-tax contributions. I understand that. But those same posts say something about teachers not having any Social Security wages deducted. At the college where I teach, they absolutely deduct social security. Does that change things regarding the TRS deduction?

 

Also, the literature says that TRS is a 401a or 403b plan. My school's benefits coordinator says it is neither of those but didn't provide further details. Can anyone elaborate on that too?