Spark with 5 volts to solder (weld) tin
Usually cheap arc welders have difficulty being set to very low current. 

Spot/resistance welders -there are good machines with specs like these (Miyachi):



This kind of machine is very expensive- probably $5-10K, and worth it for high tech manufacturing (we use them for making superconducting junctions). 

There are very cheap welders sold from China for making battery packs, and some can be used with tungsten handheld probes. Not sure about well they work, however, caveat emptor. It's easy to find them, and you may recognize the type you saw. 



Edit: 
Okay, John, that's a great video. Such dexterity- working with both hands simultaneously during the orientation phase of the operation! The 5mm spark you saw may be "HF" = High Frequency which is used to initiate the arc. Conceptually, there is a series choke which conducts the main arc well, but presents a high impedance to high frequencies allowing a high voltage to be superimposed on the low voltage welding supply. I think the operation shown in the video would not be very healthy if the solder was not RoHS- the temperatures in an arc could result in a lot of lead vapor compared to a soldering iron. Very fast though. As a buyer/factory inspector- plenty of places for human error in that process- at least the worker is wearing finger cots. You can expect the odd intermittent joint to slip through even with 100% testing. Ask them what their fallout rate is at testing and verify by looking at the size of the piles of reject units vs. production rates.