Here is the complete version of 46.02 as it reads now:
Statute text
(a) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun, illegal knife, or club if the person is not:
(1) on the person's own premises or premises under the person's control; or
(2) inside of or directly en route to a motor vehicle that is owned by the person or under the person's control.
(a-1) A person commits an offense if the person intentionally, knowingly, or recklessly carries on or about his or her person a handgun in a motor vehicle that is owned by the person or under the person's control at any time in which:
(1) the handgun is in plain view; or
(2) the person is:
(A) engaged in criminal activity, other than a Class C misdemeanor that is a violation of a law or ordinance regulating traffic;
(B) prohibited by law from possessing a firearm; or
(C) a member of a criminal street gang, as defined by Section 71.01.
(a-2) For purposes of this section, "premises" includes real property and a recreational vehicle that is being used as living quarters, regardless of whether that use is temporary or permanent. In this subsection, "recreational vehicle" means a motor vehicle primarily designed as temporary living quarters or a vehicle that contains temporary living quarters and is designed to be towed by a motor vehicle. The term includes a travel trailer, camping trailer, truck camper, motor home, and horse trailer with living quarters.
(b) Except as provided by Subsection (c), an offense under this section is a Class A misdemeanor.
(c) An offense under this section is a felony of the third degree if the offense is committed on any premises licensed or issued a permit by this state for the sale of alcoholic beverages.
I think 46.15 is too long to post in full, but the important part of it for this discussion is the same that it has always been. That part says that section 46.02 is not applicable if you are traveling.
So, if you are traveling, it has always been legal to carry concealed or open. The confusion for the past two years was that if it was open, the presumption did not apply, but the traveling exception was still there for other ways to meet its requirements. For the purposes of section 46.02, the court would consider (IMHO) riding on a motorcycle to be in a vehicle. This means that if you are on a motorcycle and have the weapon concealed, you can carry around town. If you are traveling across the state (as one example), the weapon would not have to be concealed.
Note that in this law, it specifically says that if you are in a car that you own or control, you may carry a club or illegal knife. DPS may want to interpret it differently, but I would bet it is someone relying on old laws and not really reading the new one.
AS always, I recommend a CHL to avoid most of the problems of people understanding the new laws. I also recommend not being a test case for anyone's interpretation.