I've used both approaches. I watch how a Deer moves from cover into a meadow or field and try to copy the cadence, they rarely take more than a few steps before a pause, then they step out again and repeat. I've also tried slow and steady with no pauses. I try to make like another Deer and not a predator. If there is a irregular breeze, i move when the wind is blowing and stop when it dies down. A lot of background noise, it is often the unnatural noises combined with a faint scent or movement that sets them off. It really doesn't take much sound if it is the wrong sound, like two halves of a zipper rubbing together, keys jingling etc.
Often it is a subtle noise and a faint odor that sets them off, scent more than sound. Walking the wood line, forest heats up slower than the open in the morning and stays warmer after the open cools down in the evening. If there is no breeze, the air moves subtly into the woods after the open areas cool down. Not much you can do about it, other than try to minimize your scent. And remember they can see out of the woods much better than you can see in.
Often I've spooked a Deer and had them return to nearly the same spot half an hour or three quarters of an hour later. Not always, but often enough I keep it in mind. Doe with fawn tend to spook easy and huff or bark more, part of the plan to lure a predator away. They park the fawn and then run off barking and return after awhile to pick up junior. If a Deer hears another Deer eating, they come into the open a lot less carefully.