It is interesting to see the different dive practices in different parts of the world.
In the UK it is exceptionally rare for the boat to moor into the shot line, almost unheard of.
Once at the wreck site the common practice is to shot the wreck (very few wrecks have a permanent shot on them - some popular sites like those in Scapa Flow, or around Plymouth etc may well have a shot attached).
Most shots are either a grapple, or a heavy weight.
The dive boat will then keep station near the shot, with a lookout looking for DSMB's whilst divers are in the water.
When the site is slack enough, the first pair will drop in, taking care to put minimal load on the shot. Often, they will then either hook the shot into the wreck, or use a waster line to tie the shot into the wreck.
In most cases, the last pair down ensures the shot is unhooked and free to be recovered by the boat (once all divers are out of the water), occasionally a lift bag is used to help recover heavy shots.
IF, the plan is for all divers to ascend the shot, then it will not be released by the last pair of divers on the descent.
An awful lot of UK dives do not be plan for the divers to return to the shot. The plan being that the divers will releasing a DSMB and ascending as they reach the end of their planned bottom time, drifting free of the wreck as they ascend/decompress.
On sites where an ascent is planned via the shot. There will often be a TAG in / out system. Tag in near the bottom on the way down, out as you start to ascend. If you are the last pair up you will remove the last TAG, indicating you are to ensure the shot is clear (possibly inflating the lift bag on the shot as well).
IF there was no shot when you returned for your ascent, then you would release a DSMB. You would NOT tie a DSMB in at the bottom, but ascend reeling in or spooling in the line as you go. (Tying a line in would in all likelyhood result in the DSMB being dragged back down to the seabed by the tide.)
(I have actually ascended a shot, only to meet the two buoy's at 15m because there is so much tide running they are being dragged back to the seabed - Leopoldville, Cherbourg.)
The dive boat will be keeping station near the shot, looking for DSMB's, and divers on the shot.
If you have ascended the shot, once the boat has acknowledged you, you release the shot and float downstream so that the boat can pick you up clear of the shot (and any divers).
In most cases, both divers will be expected to carry their own DSMB, and be capable of launching it solo, just in case they are separated. On a lot of boats, if there isn't one DSMB between a pair you wouldn't be allowed to dive. A lot of divers carry multiple DSMB's.