Resolved questions
Students - 同学们 or 学生?

students----学生
classmates----同学们

but, well, sometimes when teachers say "students" it may mean "同学们"

students是学生
classmates是同学

They have the same meaning, but it depends on whom you talk with.
他们的意思是一样的（除了单数和复数不一样），但取决于你说话的对象。
If you talk with a group of students, you should call them "同学们", but you cannot call them "学生/学生们".
如果你对着一群学生讲话，你要称呼他们（对方）“同学们”，但你不能称呼他们“学生/学生们”。
If you talk about a group of students with your friend, you should tell him " （那些）学生们/（那些）学生/（那些）同学", but you can't say"（那些）同学们"
如果你跟你的朋友讨论一群学生，你要跟他说“（那些）学生们（复数）/（那些）学生（单数）/（那些）同学（单数）”，而不能说“（那些）同学们（复数）”。

student 是“学生”的意思
fellow students 才是“同学”
但是将students放在课堂用语的语境中也可以用作“同学们”

学生----Students
classmate in chinese means some student in one same class ,so these students they are classmate