The relationship of the SCO (shared content object)s and the LMS (Learning management system)s is like electric appliances and power outlets from some point of view. An SCO/appliance can be used by/(plugged into) any LMS/outlet. But at any time, there can be only ONE SCO on a LMS. SCORM can be regarded as the combination of SCOs and LMSs.
Both DOM and SCORM are some kinds of object models. But both of them focus on specific goals. DOM is for dynamic document presentation, and SCORM focus on how to share educational resources among learning management systems for distance learning.