a real world point of view
An umbrella title is a title which is used to label a group of things which have all gone out under other titles.
According to Yale University it is effectively synonymous with one sense of the phrase series title. Though it should not be confused with programme title, Yale describe it as a "title for a number of objects published individually but forming a logical group as defined by the publisher".
Doctor Who examples of this ilk would certainly include: Past Doctor Adventures, Missing Adventures, New Series Adventures and so forth. Inasmuch as printed matter is concerned, there's not much difference between a series and umbrella title.
However, its usage amongst writers about television distinguishes between a simple programme or series title —like Doctor Who — and an umbrella title. In television, the term is often used as a catch-all phrase to describe a timeslot that houses many distinct, if thematically related, things. Writing about 90s American television, for instance, Tim Brooks and Earle Marsh said,
For almost seventeen years, ending in early 1999, CBS had aired a potpurri of late-night programming under the umbrella title, The CBS Late Movie.
It's thus possible to immediately label things like Doctor Who Night and Doctor Who Weekend as umbrella titles. Less obvious examples exist as well. Night and the Doctor, a collection of loosely-themed shorts on the series 6 home video releases, would also be an umbrella title, as would The Key to Time, the overarching title for season 16, and Key2Time, the audio sequel trilogy published by Big Finish. Umbrella titles are also quite common on Doctor Who DVD documentaries, as illustrated by The Making of The Trial of a Time Lord, Stripped for Action, Girls! Girls! Girls! and Now and Then — just to name a few.
It can be argued that serial titles are in fact umbrella titles as well, though this point is debatable. At the very least, it is not commonplace to hear The Rescue being referred to as an "umbrella title". Instead, such labels are generally thought of as serial titles or, more simply, story titles.