I'm not sure about everywhere else, but once a plat is set, you don't get to move the lot lines around here. You can buy Lot 10 and portion of Lot X, etc., but you're not moving the lot lines without a replat/amended plat, etc. Which is a PITA.
In most jurisdictions I've worked in and all I'm licensed in, there is an administrative process to adjust or move boundary lines between two parcels, thereby redefining the boundaries between them. Most often, the process is referred to as a Boundary Line Adjustment or (if in a subdivision) a Lot Line Adjustment.
Where I'm at in Idaho, if it's between unplatted parcels, it's a BLA. If between platted parcels (or a combination of platted and unplatted parcels), it's called a Replat. Fortunately, that's not quite as complicated as it might sound - not a full platting process although the map is titled "Replat of Lots X & Y of Aspen Acres" or some such. Still a mostly simple administrative process with relatively minimal review.
As to original survey vs resurvey, all except the newly defined boundary location would be resurvey. The survey for the BLA would be an original survey for the newly defined location of the common boundary.