Deadline day is the last day of a transfer window, ending at a fixed hour set by each league. Clubs that have a deal substantially agreed can file a deal sheet shortly before the deadline, which buys extra time to submit the remaining paperwork.
The deal sheet is the reason transfers keep being confirmed after the deadline has passed. A club that lodges one before the cut-off is telling the league the essentials are agreed and the documents are coming, and it gets a short extension to file them. It is not a way to keep negotiating.
The rush is structural rather than theatrical. Selling clubs will not release a player until they have a replacement lined up, so a chain of deals can hang on one club at the top of it deciding, and every club in the chain is waiting on someone else's decision.
That is also why late deals skew towards loans. A loan is quicker to agree, needs less due diligence and carries less risk if it goes wrong, so a club that has run out of time to buy will often borrow instead.