What exactly is a "non-archival venue" and "workshop with proceedings"?
What do people exactly mean when they say "non-archival venues" although the venue might have "publications"?
  


Usually a conference/workshop is made "non-archival" so that the research presented at the venue can be published somewhere else (either before or after the event), i.e. the venue does not require exclusivity. An author can present their work to the conference/workshop specialized community, while at the same time keep the option to publish it in another reputable venue (for instance a journal). It seems common that the venue would let the authors choose whether they want their paper to be published in the proceedings or not, in this case the proceedings are made of the papers whose authors opted in. Example: https://sites.google.com/view/acl19studentresearchworkshop/call-for-paper.


  
  What is the exact difference between "workshop with proceedings" and one without it? Is there a way to determine this without having to contact organizers?
  


The difference is literally that in one case the papers are published in the proceedings of the workshop, in the other they are not. In my experience workshops without proceedings do not require submission of a full paper, only a one page abstract for instance. There are also some conferences/workshop which don't have proceedings, but the abstracts presented can be selected for publication later as a full paper in a journal. In general this kind of information should be provided in the call for papers, but if it's not then the only way to know is to contact the organizers.