A Dumpy Level is a level that has a bubble in tandem with the telescope,and when levelled over the three footscrews will determine a back to back level around a project. It usually has a circular bubble that allows coarse levelling of the instrument before critical levelling of the tubular bubble.
It is used in conjunction with a surveyors stave and needs two operatives. Accuracy will be about 2.5mm at a 100mtrs.
An Automatic level is quite a sophisticated Level, it has a damped pendulum that has about 15' of swing back to front and sometimes has a flag comes into view to show it is out of level. Again it has a circular bubble of 20" accuracy for course levelling for setting up.
These levels nominally are about 8" accuracy and some less than 1" and to 100ths with an attached plan Plate over the OG. EG. An N3(70) from Leica.
Theodolites are now being designed and built with so many functions that we workers who repair them have a job to keep up with the technology. The latest is fitted with a TV camera that allows realtime viewing of the target and has X hairs in the pic.
Laser measuring is now the Norm with reflectorless working and accuracy to sub 1mm.
Most are now automatic and can seek out a special target, the Theodolite is left in one position and the operator walks about with the target on a pole that also determines the height of the ground at that point. As stated variations exist with GPS which is used for larger surveys and you may see them used by Police at road accidents also.
Clive