I would like to know what the difference between records and record is.
Which would be correct — John Allen's Records or John Allen's Record?
Well, briefly skipping over the fact that there are multiple definitions for the word "record", as it's fairly clear which sense you are using, there is no major difference between record/records as used in your question.
A record is a thing, often a document, constituting a piece of evidence about a past event or period.
John Allen's Records implies that John Allen has a collection of documents, diaries, observations, reports and the like, pertaining to whatever event.
John Allen's Record implies that there is one single file. However, within this file there could be an expansive collection. The singular noun suggests that if there are multiple documents, they have already been collated int a single source.
So, there is a slight difference and it could be pertinent to choose one over the other in certain situations. However, they could also be interchangeable in most cases.
I suggest: Use 'record' if you are referring to a single document from one original witness/source; otherwise, use 'records'.
Hope that helps.
N.B. Other senses of the word include plastic discs for recording data, a performance of some feat that is considered 'better' than all other performances of its kind, a summation of a person or organisation's overall performance in a given field.
There's a difference between Record and record. 'John Allen's record' would be the file on John Allen (pace Fraser Orr): 'John Allen's records' might be the collection of such files, or the various notes JA made (as Karl said): 'John Allen's Records' would have to be the name of a record shop owned by John Allen (record in the sense of black disc; ask your parents about this if necessary): I genuinely can't think of a use for 'John Allen's Record'.