Omitting the article makes the reference generic and universal. It has the same basic meaning as "any student" in this particular case, but using "any" makes you think of starting from a small number that simply has no upper limit; whereas using no article leaves the number completely open.
Saying "the students who work hard" immediately picks out a particular group of students in the speaker's mind and implicitly contrasts them with "the students who don't work hard."
Pragmatically, they are almost the same; however, here is how I would hear the message from a teacher saying these phrases at the beginning of a semester class.
"Students that work hard are likely to get good grades, so I urge all of you to put in the necessary work. I want all of you to have success."
"The students that work hard are likely to get good grades, but the many of you who treat this course too lightly are probably going to get bad grades. Decide now which group you would prefer to be in."