I think they are an amphenol type pin and socket connector system. I have a Black Line pack, but have yet to burn out a socket to look carefully and need to fix one.
The back end of each pin in such a connector has a half cup that you set the pre tinned conductor in, heat the cup side, and add solder to the open side of the cup.
Similar connectors with smaller pins for multi channel dimmer control in theatrical stage dimmers, and larger connectors for the power outputs to multiconductor cables from those same dimmers. I have soldered a lot of them.
Re- using a pre soldered connector requires a lot of solder sucking braid and a gas torch and lots of flicking the heated connector to dislodge old solder before you can think about using it again.
The big power ones I have worked on are over $120 each, so yes, you reuse them.
Be methodical. Start from the back side to the connector, towards the middle, doing the edges as you go. The biggest one I have soldered had 28 or so pins. It just takes time and patience.