In Texas, it' a Concealed HANDGUN License.
You can buy whatever you want, regardless of wheteher or not you have a CHL or not. As it is NOT a Concealed WEAPONS permit/license, it does not give you carte blanche to conceal carry everything.
Some folks will tell you it does, but that is from laymen's interpretation of the law. As there has not been a court case deciding which interpretation is correct, everyone I known, including CHL instructors advise people to carry only "legal" knives, I.e., 5.5" or less, single edged blades.
IF HB1935 passes and is signed, then we won't have these issues in the future.
For more info on that see the bill tracking thread here in the knife law forum.