Regarding dogs vs bears and other animals. My dog and I hike/walk hundreds of miles each month and have seen a wide range of animals, including a stampede of 100+ cattle and being surrounded by 50+ elk. We go to areas with unleashed dogs nearly every day and also have run in to stray dogs, seemingly feral dogs, as well unleashed dogs while hiking in remote wooded areas.
In my opinion, it’s difficult to generalize, as there is a large dependence on the context and specific animal. For example, earlier this year, we came across a wolf-dog in the woods, maybe 70% dog and 30% wolf. It was much larger and more physically threatening than a typical dog – easily over 100lb. It also appeared to be aggressive and ignoring my dog’s body language (my dog initially acts submissive towards physically threatening dogs that she doesn’t know). Fortunately the other dog was on leash. However, the owner warned me she didn’t have physical control over her dog due the size/strength, so we should leave quickly. I certainly wouldn’t want to have run in to that dog off leash.
A short time later, I ran into a stray beagle in my yard. I felt comfortable enough to take the beagle inside my home, give it food/water, and hold it until I could find the owner. It was clearly a neighborhood pet and displayed no aggressive body language or behavior.
In both cases above, the dogs appeared to have no fear of humans and were comfortable approaching humans. This differs from most mammals in the wild. My experience with non-dog animals in the wild is they usually do some combination of avoid us, ignore us, monitor us, or warn us (for example, a young bull might scratch the ground a few times and run a few steps towards us, then stop, and return back to his group),; but unlike dogs, the wild animals don’t intentionally get close to us .
The context above also involves having my dog with me. I am concerned with both how my dog will react to the wild animal and how the wild animal will react to my dog. A person who is hiking alone might feel differently, as might a jogger or trail runner who is concerned with which animals might chase them with prey instinct. What is expected and unexpected also is important, as is the distance away. For example, I’d prefer running in to a stray dog on the walking trail behind my suburban neighborhood house than a stray bear on the trail. However, if I’d prefer to see a black bear in the woods from a long distance away than a stray dog in the distance.
Among the animals that I see on a regular basis, the one that most concerns me is rattlesnakes. I know my dog won’t approach or even make eye contact with a much bigger animal like horses, cows, or bears. She is interested in some animals her size like coyotes and bobcats and may want to follow them, but she’ll stay a good distance away, won’t initiate anything, and will back off if they do anything threatening. I’ll also have time to intervene and/or call back. However, I think there is a good risk of being bitten by a rattlesnake… My experience is rattlesnakes often fall in to the “warn us” grouping above, and I’m not certain that my dog would always follow the warning, and/or she might already be too close when the warning occurs. There is also a risk of unintentionally stepping on them. I have seen multiple rattlesnakes seemingly sleeping, with head in bush/hole and body spread out across trail in warm sunlight. If I was not looking where I was going, I would have stepped on them.