"Dip and dunk" refers to the processing of the film and has nothing whatsoever to do with printing.

"Machine-printing" used to mean (in UK, where I worked in a "pro" lab) that the negs were printed using a projection-printing machine which would adjust exposure based on an average of the neg brightness. There were also similar machines with a vdu that enabled manual corrections for each shot, but in that case any lab would mention "individually corrected" or something like that to indicate added value (and a higher price).

One thing you will face is that different lab operators will use different terms for the same service, and vice-versa. The only way to know what is going on is to go there and ask. For small colour enprints, the standard dev-and-print of a complete roll of film, then the scan and print system can work fine. Variations will come from the skill of the operators and the maintenance of the machines. "Best" results will be from optical enlargements on appropriate paper generally, but Lightjet RA4 prints can be impressive indeed and open up some size options which would be difficult by hand.