A theodolite is a precision instrument that measures vertical and horizontal angles, especially in triangulation networks. A transit is a simple form of a theodolite that comes equipped with a telescope but lacking in features such as mechanical meters and scale magnification.
Theodolites can rotate on their vertical and horizontal axes and have a lot in common with transits. Typically, transits have telescopes that can flip over to double angles and allow easy back-sighting. However, transits have less precision than theodolites, and their importance keeps decreasing as more compact and accurate theodolites become widespread. Both theodolites and transits have uses in the surveying industry and can be used for the same projects.