You can try it any way you wish. We all have different goals and circumstances. Some people may be horrified that you'd even think of managing them a certain way but someone else will say, yeah, that's exactly what I do.
If I do a tractor, do I need a Coop? I feel like the birds wont be protected in a tractor at night.
This depends on your tractor. You can build them so you can securely lock them up at night. You can build them with nests and a roost area protected from weather. Some people surround the tractor with electric netting. There are just all kinds of different things you can do.
If I don't do a tractor, do I really need a run? Why can't I just build a coop with laying boxes and let them roam in the pasture/woods in the day?
You absolutely can. That's how Dad managed his chickens, a coop for night and no run during the day. Some even slept in trees. The obvious risk to this is that you get predators attacking during the day. It might be nice to have a run so you could safely lock them up while you dealt with the predator, some are not easy and take time.
I only remember Dad dealing with two predator attacks. A dog showed up and killed several chickens before it was shot. A fox started picking off one chicken every morning just after sunrise. It took Dad a couple of days to determine its pattern and then he shot it. All in all that wasn't too bad. But some people that try that will get wiped out almost immediately. Say a pack or coyotes or dogs show up. You just never know when that night happen. But say a bobcat, fox, or something like that starts picking off one a day having a run to protect them might be handy.