From GunsSaveLives.com:

Think of it like this – if you have a driver’s license in your home state, you can use that anywhere in the country, however, you still have to follow any state driving laws in other states. Just because your state allows right turns on red doesn’t mean another state does too.

Cornyn’s Senate website:

U.S. Sen. John Cornyn (R-TX) today introduced the bipartisan Constitutional Concealed Carry Reciprocity Act of 2015, which would allow individuals with concealed carry privileges in their home state to exercise those rights in any other state that also has concealed carry laws, while abiding by that state’s concealed carry laws. Senators Joe Manchin (D-WV), John Thune (R-SD) and David Vitter (R-LA) are the lead cosponsors of the bill.