Does contributing to my Thrift Savings Plan Count towards Contributing towards my Roth and Traditional IRA?

No, the federal TSP is not a Roth or traditional IRA.  Enter amounts shown in box 12 of your W-2 only in box 12 of TurboTax's W-2 form, nowhere else in TurboTax.

No, it is not the same thing.

If you are asking because you want to know if it qualifies for a Saver's Credit, then, YES.

Depending on your adjusted gross income reported on your Form 1040 series return, the amount of the credit is 50%, 20% or 10% of:

• contributions you make to a traditional or Roth IRA,
• elective salary deferral contributions to a 401(k), 403(b), governmental 457(b), SARSEP, or SIMPLE plan,
• voluntary after-tax employee contributions made to a qualified retirement plan (including the federal Thrift Savings Plan) or 403(b) plan,
• contributions to a 501(c)(18)(D) plan, or
• contributions made to an ABLE account for which you are the designated beneficiary (beginning in 2018).