A watch sold with all of its original accessories: box, papers, warranty card, and often extras like tags, links, and the original purchase receipt. A stronger claim than box-and-papers alone.
Full set is the collector's shorthand for a watch accompanied by everything it originally came with: the outer and inner boxes, warranty card, instruction booklet, hang tags, spare bracelet links, and sometimes the original sales receipt. It's a broader claim than box-and-papers, which technically only guarantees the box and warranty documentation specifically.
A genuine full set can meaningfully affect resale value, particularly for vintage and limited-production pieces, since the accessories confirm provenance and are far more easily lost or discarded over decades than the watch itself.
Box and papers technically refers just to the outer box and warranty documentation. Full set is a broader claim covering everything the watch originally shipped with, tags, spare links, booklets, and sometimes the original receipt.
Often, yes, particularly for vintage or limited-production watches, since the accessories confirm provenance and are much more likely to have been lost over the years than the watch itself.
Boxes, tags, and paperwork are easy to misplace or discard over decades of ownership in a way the watch itself typically isn't, so a genuine, complete full set becomes harder to find as a watch ages.