The orthopedic examination is very similar and both are looking to see how structure affects function. OMM looks much closer at somatic dysfuction in the spine or periphery and how manipulation or soft tissue techniques can reestablish correct structure or normalize sympathethic or parasympathetic tone. PT uses much less to no soft tissue or manipulation techniques, but relies much more on exercises specifically directed at certain muscle groups to reestablish correct biokinematics. OMM is a very passive treatment with the exception of the patient contracting their muscles during muscle energy techniques. PT is much more active treatment having the patient performing exercises that will ultimately translate into the patient having less pain, better mobility and more independent activities of daily living. A DO has minutes to perform a musculoskeletal evaluation and treatment, so they must be very quick and to the point during their sessions, whereas a therapist has up to an hour sometimes for an initial evaluation and multiple follow-up sessions lasting weeks to months to work on a patient's functional problems. While there are many other differences between the two, OMM puts a lot of the responsiblity for patient outcome on the practitioner, whereas the PT's goal is to intitially hand-hold, but to ultimately educate the patient to become as independent as possible.
Your summary seems accurate except that I know many PTs who use soft tissue manipulation on many of their patients. They might only need to do so a handful of times (or less) in the course of treatment of a single patient, but I think saying they use it "much less to none" may not present the whole story to the OP. Perhaps the difference in our opinions lies in sampling error or subjective definition of "how much."
I am a PT gone back to osteopathic medical school. I used soft tissue techniques when appropriate, but PTs know to only use it sporadically because the patient often becomes dependent on the modality. The hands-on stuff makes the patient feel good, but it is the exercise and patient willingness and motivation that will ultimately turn into long term results, and that is why the majority if not all PT sessions are devoted to the exercise component. I have worked with many PTs, PTAs, and aides, and all of them use active exercises as their go to treatments, and may or may not use any soft tissue modalities, especially in settings such as inpatient rehab, acute care, or SNF units. DO's utilize manipulation and soft tissue work as their first line of treatment concerning the MSK system and occassionally prescribe home exercises or PT. I do agree that more PTs are starting to venture into a more hands-on approach and are feeling resistance with chiropractors and even medical physicians as they try to gain more autonomy with services they offer, but this is much more of an issue in outpatient and private practices.