There is a fine line between the two. Credentialing is how you are vetted---submit copies of diplomas, residency certificates, board certifications, licenses, etc. so they verify that you are who you say you are, and that you have the training required to do the job you're being hired for. This also involves calling all programs you trained at (which is why stuff that happens in residency can haunt you, should you leave on bad terms) and all places you've worked previously to make sure you are competent and have no red flags. The criminal background check is also part of this (I personally don't remember having a credit check, but this can be part of the process too). This gets more time consuming for the person doing the credentialing as the list of "where you've been" gets longer.
Privileging is how they delineate or itemize WHAT you are allowed to do. I'm a surgeon, so my privilege list is longer than that of some other fields (specifically it states I can admit, consult, give sedation, lists the procedures and organs I am allowed to work on, etc.), but does not include things that fall outside of my scope of practice like hip replacements or cataract procedures. My privilege list for the clinic setting is different from my hospital privilege list. Most specialties have a basic privilege list that has stuff you can cross off or add to the list, and some have additional privileges listed that can be checked off but may require extra proof of training, volume or CMEs to maintain (for example, if a general surgeon also wants to do vascular or thoracic, or anyone wants to do an unusual procedure that is not covered by their basic list). There were a couple things on my "basic privilege" list that I crossed off because I had no intention of doing them, or had no experience with. The caveat to this is that it is much, much easier to get a privilege to start with, than it is to add it later on, so don't cross anything off that you even remotely think you may want to do. I had a copy of my procedures from residency that I submitted to prove I had experience doing things I wanted privileges for; if I change jobs, odds are they will want a list of procedures I've done for the last x number of years on file before granting me privileges. Usually a physician (dept chair or medical affairs head) has to sign off on privileges to ensure they are appropriate. Where I work, the same secretaries who do all the physician credentialing and privileging records also take care of renewing our licenses, DEAs, insurance company forms, etc. on our behalf.
Bottom line:
1. save copies of your diplomas, certificates, licenses and other stuff (even copies of stuff like ACLS/PALS/ATLS/etc. might come in handy) so you can submit these easily to those who request it. Scanning and saving copies electronically will make your life easier in this respect.
2. save copies of case log/procedures done or other stuff you have to track in residency so if you are asked for it down the road, you have it. This is especially important for procedure based fields.
3. save copies of the same once in practice, so if you change jobs, you have a current record and aren't scrambling. Your clinic or hospital may be able to pull this info for you as well, but then you are depending on them to do this in a timely and accurate fashion. I get a printout every month of what I've billed, so something like this could be used to provide a record too.
4. Once in practice, consider scanning or logging your CME credits, as this is also needed to maintain board certification, or in case you get audited by your licensing board (this happened to me and was a big PITA....they wanted a list and copies of all certificates on short notice. OTOH, it made it easy later on when I had to submit info 8 months later to show I was fulfilling MOC for my BC)