"References" means a list of people, with complete address, phone number, and email, who are willing to comment knowledgably about your work in some area--that is, they can speak to the quality and context of your creative writing, your teaching, or your service work. At their best, references--which imply that these people named are also willing to write letters of recommendation on your behalf as well as answer phone calls--are a form of mentoring. At their worst, they sound like name-dropping, and if they are can often backfire as a result.
While not a part of your vita, "Letters of Recommendation" are normally what your references write for you to carry forward into the world as what used to be called letters of introduction. These are letters that say to the world what this person thinks of you. They often accompany your vita, or follow soon afterward if the person to whom you are submitting your vita is interested. These letters are important documents, not always for what they say, but in that they exist. Presumably the person writing a letter is saying good things about you.
References do not necessarily all write letters for you, however. They may simply be available should someone want to do a reference check on you--are you who you say you are, did you work at this institution, and so on. This is a straightforward reference check and these phone calls go on all the time. They may also be a follow-up on a letter of recommendation.
References are listed at the end of your vita, but letters of recommendation are separate documents. A prospective employer may or may not want to see letters of recommendation. Often you will have sent a placement file, if you are applying for a teaching job. This file would include your vita and letters of recommendation together in one presentation.
In terms of your vita, understand that you must not simply list people as references without their knowledge. You must ask their permission, and make clear what you are doing. You may, at the same time, ask for a letter of recommendation, though choosing to wait until you are actually on the job market or pursuing some kind of support may be a better idea, as the letter may be more up to date.
Choosing your references is important, and much can be read into your choices. If you are in academia, it is logically imperative that the Chair of your committee be a reference. If your Chair is not a reference, that suggests some likely trouble. Normally, this is the person who should be your staunchest advocate, and so the question of why your Chair is not a reference begs to be asked. Be warned.
"If the world were a logical place, men would ride side-saddle."--Rita Mae Brown
The other choices for references depend on what you are doing. If you are applying for a teaching job, then you need to have someone in the group who can address your teaching. If it is an arts administration job, again, you must have someone who can talk about your work or your potential in this area. The pattern is logical enough here. All your references need not be from one institution or job site. They should simply be the best choices for you.
Three references are a minimum, and reasonably standard. You may have five, six, or even seven, but any more than that is overkill, and unnecessary. Rank them in the order you would like them contacted.
"References Available Upon Request" is a common entry at the end of a vita. This way you do not need to list the references--which in fact may be a changeable list. You may choose to wait until you are asked.