The correct answer is the second statement: "The border between Alaska and British Columbia is a thick line, indicating an international border.".
Alaska is an American state and British Columbia is a province of Canada. Although both are administrative divisions of their respective countries, they belong to different nations and the demarcation is made by a thick line, which represents an international border.
As both Texas and New Mexico are states within the United States of America, these subnational entities are under the jurisdiction of the same country and thus this division is demarcated in the map by a thin line, which indicates a state border.