The Hirose DF12E(3.0)-10DP-0.5V(81) is a 10-position header with outer shroud contacts from the DF12 series, designed for parallel board-to-board stacking. The 0.50 mm pitch and 3 mm mated stacking height define the z-height budget between two PCBs — the 0.091" (2.30 mm) height above board tells you how far the header stands off the bottom board before the receptacle mates.
If your existing design uses a different stack height (say 4 mm or 5 mm), this header won't fill the gap without changing the receptacle or adding a spacer. The dual-row arrangement with 10 positions gives 5 contacts per row, which is typical for a narrow signal bus or a small parallel interface.
The DF12E(3.0)-10DP-0.5V(80) shares the same 10-position count, 0.50 mm pitch, 3 mm stacking height, and gold contact finish. For a pick-and-place line running reels, the (81) is the one you want; for hand-assembly or low-volume builds, the packaging difference may not matter. Both are obsolete, so sourcing either depends on broker availability.