You are correct to infer that the two have some core similarities, although as you implied, there are also some important differences, with PO having more of an identity bent as compared to OC. (Anecdotally, imagine the employee who is highly committed to remaining with his/her company - possibly for a myriad of reasons - but does not necessarily personally identify with the company). Some research has indicated that PO may be predictive of OC (see Han et al., 2010; Liu et al., 2012). There is a good recent review of PO in JOB (Dawkins et al., 2017) that will point you toward some more relevant studies including those I noted above.
There's another thing to keep in mind. Sometime PO and OC are not correlated at all. Remember organizations are made of different divisions, as well as different occupations. One can have PO for their division, but have little to none OC overall for the larger organization. Same with PO and one's occupation. One might be completely sold on their career, but have no commitment to the particular organization currently worked at.