The popular vernacular uses 'rejection', 'denial', and 'refusal' interchangeably. They mean that their application was accepted and processed as legitimate but failed at the decision making stage. A indication is made on the applicant's passport and it is returned to the applicant.
But from a practitioner's point of view the terms 'rejection', 'denial', and 'refusal' all have different meanings, and using the correct meanings enhances the site's credibility.
'visa-refusal' can be defined as: A refused application is a valid application which has been processed and the decision-maker has decided that the applicant fails to meet the requirements. For example, if the applicant has not demonstrated the required level of funds in their bank account or has submitted a translation which does not meet the requirements or has submitted a photocopy rather than an original document. When an application is refused, the passport is usually marked to show what has taken place and more importantly, a record is made in the sovereign's computer system.
'visa-rejection' can be defined as: An invalid application that did not reach the decision stage for any number of reasons: the wrong form was used, or the pictures were not in the correct format, or the bank declined to pay the credit card, or countless other reasons that can make an application invalid. When an application is rejected,, it will be returned unprocessed with the fee payment not taken or refunded. It will be as if an application had never been made.
In Regulation (EC) No 810/2009 (Schengen rules), the word 'refusal' occurs 12 times. The word 'rejection' is used once in a context about verifying entry conditions. The corpus of UK law and guidance uses only the word 'refusal' (This follows their policy that invalid applications should be refused rather than rejected whenever they get the chance).
The US State Department uses 'denied' and 'denials' interchangeably in their brochures as a synonym for 'refusal', but they are known formally as 'refusals' (for example their statistical reports).
In the current state of play Travel.SE uses the 'visa-rejection' tag as an all inclusive tag, and the word 'denied' in the tag definition. It's confusing. In truth, I haven't seen a question marked 'visa-rejection' that didn't REALLY mean 'visa-refusal'.
'visa-refusal' becomes the tag for an application that has failed at the decision-making stage.
'visa-rejection' becomes the tag for an application that did not reach the decision-making stage and was returned to the applicant.
OPTIONAL 'visa-denial'is a tag synonym for 'visa-refusal'
A related tag for which I have seen about 3 questions is when somebody gets bounced from a port of entry. The popular vernacular for those situations is 'deportation', but it's demeaning and horribly wrong. The correct tag is 'administrative-removal' because that's what happens when an individual fails their landing interview. You need to be convicted of a serious crime and serve a custodial sentence before you can be 'deported'.
Finally, the two other terms are 'visa-annulment' and 'visa-cancellation', but nobody has asked questions about these and so they do not need to be tags at the moment.
Sources: 'Butterworths Handbook on Immigration Law' http://books.google.co.uk/books/about/Butterworths_Handbook_on_Immigration_Law.html?id=b2LONQAACAAJ&redir_esc=y
Secondary source: Immigration Law Handbook (Phelan and Gillespie) http://www.rakuten.co.uk/shop/speedyhen/product/ST0199659702/?sku=ST0199659702&sclid=a_pla_uk&pup_e=1&pup_ptid=105540316405&pup_kw=&pup_c=pla&pup_id=ST0199659702&gclid=CNqSkrqRqcICFWfKtAodOFEA_Q