Categorical training leads to eligibility for board certification.
Preliminary programs do not lead to eligibility for board certification, and do not count against the funding "clock" for Medicare reimbursement (which goes on the categorical track one follows). Most preliminary positions are in internal medicine and general surgery, but there are also peds and ob/gyn prelims, and a first year of family medicine can be counted as one.
Transitional programs are a specific type of preliminary program that have a set number of required rotations, including ICU time, and typically a lot of electives that are free for the person to take across all disciplines of medicine (provided one isn't repeated). For example, someone going into radiology and someone going into ophthalmology might be in the same transitional program, taking the same required core rotations, but the rads person may rotate on MSK, CT, MRI, neurorads, and interventional, whereas the optho person may rotate on cornea, retina, and ENT.