How much space do you have? Is there a clear space of at least 5 foot by 10 foot, that you could use? It doesn't even need to be entirely clear, just enough that you can move without constantly tripping. Hallways can serve the purpose if you don't have room in your apartment. This is what I do in inclement weather, or when I don't feel like dressing up to work out (obviously less feasible for the hallway method).
Alternately, if you feel that you must practice in place, walking in place is just a matter of picking up your feet alternately. Unlike running or jogging, you always have one foot on the ground. As with other forms of stationary exercise, I'd advise lifting your knees a bit more to compensate for not having the extra effort of actually moving.
As for differentiating running and jogging... honestly, that's largely a matter of semantics. For the purpose of stationary exercise, they're basically the same thing, just a matter of how intensely you're moving.
Either way, you will likely be using the time method rather than the distance method, really not an issue.