I can give a worst-case scenario from a staff perspective: All departments will talk about students to some degree in most higher education establishments. By bulk they tend to be general observations or discussion of where support is needed, or where somebody needs particular investment in time to reach their potential.
There is certainly no best practice when it comes to talking about students generally, both in work hours and out-with, but recorded messages such as email and intranet are generally a big no-no as it can be recovered at a later date as part of a SAR. Now this would suggest that professors/lecturers are of the mind that what we say can be malicious or more conductive to personal intent of harm rather than objectively making things the best for every student, both emotionally and academically.
Things tend to reach a breaking point when dealing with problem students. We had a situation where a mature student returned to University for a career change in a new subject in order to gain the correct 'letters' to pursue a career they had already achieved relative acclaim in over a number of years. Indeed, in some subject areas they were better known and more respected than some of the staff that then found themselves appointed to teach the student.
Some staff had prior knowledge of the student whilst others were oblivious. As the department was quite small then it compounded the level of discussion on students between the close-knit staff, and especially so when so few students take it forward to honours. What I found was that the semester started off with insightful ideas from the student which were unexpected by some staff. This led to hot discussions over coffee about the gratitude of having a potential once in a lifetime innovator on our hands. Over coming weeks two of the staff actually started a campaign of complaints of arrogance about the student and the pestering of staff.
By the time of coursework grading there was a complaint lodged by the student about an essay where they were marked as a Low B when the student (who had marked work and worked in editing journal articles previously) suggested the essay could be no less than a mid to upper A. Naturally with an appeal in place another member of staff marked the essay and corroborated their colleagues result. It later turned out that the student was externally upgraded to nearly the topmost grade and the report was that the bulk of the downgrading relied upon staff not understanding the essay's concepts and questioning the style of English, and the verdict was that the English used was erudite and the use of unusual words which were very specific and relevant were considered the most economic use of English. In other words the student was using such good English and novel ideas that instead of lecturers realizing a dense read on their part with new research ideas, they mistook the work for poor grammar and making hyperbolic conclusions not supported in published literature.
Like most establishments we employ blind-marking, yet the amount of background staff communication led to the student's identity code being 'shared' which probably impacted on the marking. I think with this scenario the lesson became apparent that regardless of the reason and expertise of the experienced staff circle, the human drawbacks of jealousy and lack of acumin ultimately infiltrated and led to the gross mistreatment of a gifted student. The student became aware of the unusual change in behaviour across the staff body, which alongside the complaint concerning the essay then led to a legal complaint and enquiry which lost the institution several tens of thousands of pounds and two dismissals of staff. The student is now at a certain more famous university and the establishment narrowly avoided a scandal in media. So yes, to answer your question; Staff do talk about students, and the worry for students is it only gets bad when we discuss problem students. Some students are generally resentful and wish to cause trouble, but sometimes the genius students get severe mistreatment at the hands of resentful staff.