I was just trolling on this topic myself, because I've been asked very recently to participate in an upcoming end-of-project "Delta Analysis", which I'd also never heard of (in this context at least) and I was searching for any examples, samples or templates to help guide/direct me on the topic. I came across this thread here on Modern Analyst.
The context that is being used for the session in which I've been asked to participate is a sort of "Lessons Learned" session, where we the participants have been asked to enumerate "what was done right/well/good" and also "what we would change" (hence, I guess, the "Delta" part of it....).
Yeah, it could be considered a sort of "gap analysis", but I'm assuming it's more like a typical "Lessons Learned" kind of forum.
At any rate, thought I'd leave this with you re: my understanding over the years on the oft-used term "delta":
Delta in our BA world/industry typically generally means the same as the mathematical definition, basically, any incremental change in a variable, and is often referred to as the greek letter in the alphabet for "D" which = Δ.
As a result of this general definition, I've seen and heard "delta" used when there are scope, schedule, budget, risk, issue and resource changes that happen throughout a project, for various reasons, and the "delta analysis" is just another term for "gap analysis" or, in the case of issue (and sometime risk) management, good old fashioned root cause analysis (RCA). I don't know why in our industry we always have to re-invent the wheel and come up with new terms/words for the same things...