Continuity is film industry jargon and also important in novels. I'll defer to Wikipedia's definition:
In fiction . . . consistency of the characteristics of persons, plot, objects, and places seen by the reader or viewer over some period of time. It is of relevance to several media.
Continuity is particularly a concern in the production of film and television due to the difficulty of rectifying an error in continuity after shooting has wrapped up ...
All of this is done so that ideally all related shots can match, despite perhaps parts being shot thousands of miles and several months apart. It is a less conspicuous job, though, because if done perfectly, no one will ever notice.
At one point in my varied career life I was interested in costuming in the film industry and took some courses in this regard. I think it was after I had watched the A & E version of Pride and Prejudice (the one with Jennifer Ehle and Colin Firth) and became enamoured with the the Regency costumes. That was before I realized that filming is glamourous only in the eyes of those outside the industry. The reality--except for the big stars--involves long, sometimes very long days and nights, shooting and re-shooting. But I digress.
Because filming is non-linear--that is, not shot in sequence like a play--actors take their outfits off and on. Continuity requires that the outfit look identical each time. Or if the actor takes part of the costume off or gets a stain on it, that feature must continue in the next scene. To this end photographs are taken after each scene. Now multiply that by twenty actors in a Regency costume drama and you will feel the glamour oozing away. Costume 'bibles' are developed with photographs and descriptions for every small scene.
Many of us have laughed or smirked at bloopers showing an error on the part of the costume department. I seem to recall much was made of a scene from one of the Lord of the Rings movies wherein Sam was wearing a vest in one scene and not in the next scene, even though the sequence was continuing. I believe the director had them reshoot three days worth of film to correct the error, but that was Peter Jackson with an unlimited budget. I don't know if that would always be done.
I'm now working on continuity on my latest novel so this was what twigged the memory. No photographs are involved for me though, just careful re-reading and written notes to hopefully keep the book error-free.