A 403B is a type of workplace retirement plan. There are many types of workplace plans, including 457b, 401(k), 401(a), and 403B. 403B plans are typically offered by government and nonprofit employers like universities. All workplace plans are different from IRAs even though they have a similar purpose. If you don't know what kind of plan you have, ask your HR department or the plan broker.
Contributions to a workplace plan are reported automatically on your W-2 and captured by Turbotax, you don't enter them separately. They will be reported in box 12 with code E or BB.
If you have a 1099-R, simply report it as-is with the information and codes on the 1099-R.