One way to hold this phrase: tourism is travel, and health is the reason for it. The point of the trip is not the view but the body. From there the two meanings are just two reasons a body might send you abroad — to be treated, or to be looked after.
Two branches
跨過國界去看病
身體出問題，於是人跟著跨國移動。這一支的重點在「便宜或免費的醫療」，也因此帶上了爭議。
noun · B2
Travelling to another country in order to get medical treatment there, because the treatment is cheap or free. People usually choose this phrase when they think the visitors should not be getting that care.
跨國就醫（多帶批評語氣）
把假期花在身體上
一樣是為了身體出門，但人是健康的。這一支的重點在「度假」，所以語氣是正面的、是廣告用語。
noun · B2
Taking a holiday that is built around your body and your health — for example a trip where you do sports and exercise, or one where you have beauty and spa treatments.
健康旅遊、養生旅遊