I know one obvious translation would be "classmate." However, I have also heard the above words used when two people have had the same teacher. For example, if someone had the same teacher as you ten years ago, he is your 师兄. Since you two were never in fact classmates, is there a more precise translation than "classmate"?
I don't think there is a translation into standard English.
In some regional dialects (India, Singapore, maybe some other places) you hear people using the words "junior" and "senior", which roughly mean "person who goes/went to the same school of a lower/higher year". E.g. "she is my senior".
In very informal situations you can use the Japanese loanwords senpai and kohai which have the same meaning.
"Classmate" is not a good translation as it doesn't have the junior/senior connotation.
junior/senior/senpai/kohai are probably the closest direct translations.
We sometimes think of students and teachers as belonging to a family tree.
In this context, your 师兄 or 师弟 is your "academic brother" and your 师姐 or 师妹 is your "academic sister"; together they are your "academic siblings".
Jones is actually Qin’s academic brother, meaning that they both studied at the University of Florida and shared the same PhD advisor, Jim Hobert.
From Academic Conferences to the Classroom
I should note this terminology is generally reserved for graduate students.
You could say e.g. "academic older brother", but it's ambiguous as to whether or not this refers to their actual age, or their academic age (study level).
Beyond this, your teacher is your "academic father" or "academic mother", and you can have "academic children" of your own (should you go on to be a teacher yourself).
I am not familiar with the Chinese words provided enough to completely understand their mean but I think the online dictionary did a pretty good job at helping me understand the meaning.
Master-disciple is more of a teacher-student relationship but not in school. That relationship is similar to the teacher-student one in school but not in school. It could be one at work where one is senior and the other is junior, one is experienced and really knows what they are doing and the other has no experience to very little experience. Sometimes one might use the title "apprentice" instead of "disciple".
Mentor-protege can be in a work environment but can also be among friends or acquaintances where one is just helping the other learn something well and often working side by side in learning it.