1 In Chinese actually we don't have a very accurate concept about singular and plural like English,
eg 这些是我的学生 (These are my students) 他是我的学生 (He is my student) But you could also say 这些是我的学生们 it's no problem.
2 A simple way to tell these two words is that 同学 >> classmate, 学生 >> student
However few situation in Chinese are steady, unchangeable. Pretend that a teacher is talking to his students 'hi everyone, good morning' so in Chinese it's probably >> 嗨大家好/ 嗨同学们,早上好 Although the kids are his students, he won't say 学生 but 同学 in this context.
About sir Benjamin's answer,
>> 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" <<
I don't understand, if you think 那些同学 here is appropriate, why not 那些同学们? It's contradictory, I would say I guess only 那些学生 or 那些学生们 sound more natural into the context sir Benjamin sets.