An object is stable. A rock is an object. Water is an object if it is in a container. A rigid rod is an object.
A subject changes. A person is a subject. Air is a subject since it keeps moving. A clock is a subject.
The grammatical subject and object are distinguished in a sentence, though they both may be things. For example, “The rock rolled down the hill.” Both the rock and the hill are things, that is objects, but in the sentence the rock is the subject and the hill is the object.
Objects are acted upon. A predicate is required to go with an object. An object apart from a sentence is a thing, something passive.
Subjects are active. A verb is required to go with a subject. A subject apart from a sentence is still a potential change agent.
Space is like an object and time is like a subject. If we start with objects and then discuss their motions, we are beginning with the passive objects of space and then adding the active subjects of time. If we start with subjects, we get their motions, too, and may then bring in the objects of space. That is beginning with an active time and adding the passive objects of space.
A reference motion must be active and so include a subject. A comparative motion is passive in relation to the reference motion and so must include an object.
Bodies and things may be subjects or objects, though many are usually one or the other. The difference is in whether they change or move. An object need not move. A subject is usually moving.
Objects are spatial. Subjects are temporal. Space never moves. Time always moves.