With a Lambda. one sets Dmin and Dmax aim points into the program and a density sweep is done laying down a 21 step grey step tablet.. The operator(me) then runs the step wedge through an onboard densitometer which balances the Red Green and Blue Laser so their curve shapes are balanced and neutral in each step.
Once calibrated you send your files to print
The lambda does have onboard density , colour and contrast control, but they are much cruder than using Photoshop.
All major contrast density and colour corrections are done in PS first with a calibrated monitor, profiles are applied then minor density and colour changes are done on the Lambda. We are usually 1 or two points colour correction with the final tweak... Some of the Old Timers here who used colour enlargers know thats pretty tight.
What is interesting when calibrating or profiling is the Human Eye is much more accurate than the software and slight tweaking of colour is always preferred as a final test. You hear of perfect monitor and perfect profiles , but there always is the final touch.
Its like the old days of interneg balancing.. I remember four ways of calibrating but always in the end once calibrated we would manually look for crosscurves on a graduated background print and make the final adjustment.
Some of the digital papers we use are totally ok for enlarger projection and printing and in fact I am thinking of a project where I actually want to make an enlarger print over a lambda version.
11x14 or 8x10 colour neg to about 20 x24 print.
In digital printing they don't generally do the curve corrections in Photoshop, but rather the driver software for the printer has a linearization function. In essence each channel of RGB gets its own curve. At least that's how the LightJet I'm familiar with works.
I imagine this lets the paper manufacturer have much more leeway in the tolerances for the paper. In essence crossover can be eliminated at the printing stage. Also papers such as what Drew described above could be made to work perfectly fine for regular photos. Of course you could also tweak the output curves for the printer to get really dense blacks and crisp whites. So I guess digital only papers let them ship crap assuming the printer will take care of it. Maybe I'm too cynical.