https://www.amtrakcascades.com/riders-guide
Travelers crossing from Canada into the U.S. on Amtrak Cascades trains AND are NOT U.S. or Canadian citizens nor have a valid visa, MUST have an approved ESTA, otherwise a paper form CBP I-94 will be required. If you are a VWP (Visa Waiver Program) traveler, this applies to you. (Amtrak Cascades trains do not fall under the U.S. CBP “Land Border Crossing” definition.)
這條火車線是在溫哥華火車站就要預先清關(入美國關),而不是在邊界那裏才清關,所以不被視為一般的陸路進入美國,因此要先申請好ESTA。
美國回加拿大就是沿用你之前在加拿大給的停留期限,不需要填什麼表格。