Bear Safety
tl;dr version, Brown bears are grizzly bears and (almost) never attack people in groups. If threatened, DO NOT RUN, make yourself look big. If it charges, DO NOT RUN, make noise, wave your arms, as bluff charges are common. If it attacks, curl up, cover your head, and play dead. If you see a baby bear (ah....so cute) IMMEDIATELY look for momma and back away from the cub and hope you don't find out why overly protective moms are called "Momma bears".
As a long-time backpacker, bear safety is something I'm very familiar with. On our last backpacking trip on the Appalachian Trail, we had bears outside our tents 5 nights in a row.
The difference between the AT and Tetons is the type of bear. On the AT, we only see black bears. In the Tetons, the bears are mostly brown bears, which are a whole different animal!
While they still deserve respect, black bears are closer to giant raccoons than what most people think of as bears. They are very rarely aggressive and easily scared off UNLESS they are with their cubs. If they are with cubs, they become a whole different beast. That "Momma bear" label is well deserved and you don't want to see it firsthand. In fact, in the past decade, in the US, most attacks were momma bear-related due to people not respecting them. Seeing this chart makes me wonder if these people's last words were all, "What a cute little bear, let's get a picture with him!"
Brown bears are a whole different category of danger. It is funny because most people don't hear brown bear and think "scary animal". As a parent, I personally read "Brown bear, brown bear, what do you see?" to my daughter 100 times and cringed a little every time. So brown bears go by a few other names that are more recognizable and generally invoke more appropriate reactions. Brown bear sounds friendly but how about Grizzly Bear or Kodiak? These are different names for the same thing.
How you should respond to brown bears is very different than black bears so it is important to be able to tell them apart. Brown bears tend to be larger, they tend to be brownish, the have a very obvious hump, and they have cute teddy bear ears! Since a large male black bear isn't much different in size than a female brown bear, don't go just by size. The color and the hump are the biggest giveaways.
As for how to respond, the base response is the same. Respect them, give them room but do not turn your back on them or run, and make yourself look big. Very rarely, bears will do something called a bluff charge, where they run towards you. This is to see how you react. DO NOT RUN WHEN THEY DO THIS! You can't outrun them and they are just testing you. Stand your ground and make noise!
So that part is the same between black and grizzly bears. The part that is different is what to do if actually attacked! For a black bear, FIGHT BACK. Hit it, punch it, elbow it, yell at it, and they will almost always flee. For a grizzly bear, fall down and play dead. They most likely aren't interested in eating you but rather, just defending his territory.
SO, now for the good news! Grizzly bear attacks are very rare. Most happen in Canada or Alaska and, almost ALL happen on people alone. In the past decade, there was only 1 death from a grizzly on someone in a group, and even that one gets an asterisk because the bear killed them by pushing them off a cliff.
Also, fun fact! If you encounter an aggressive grizzly, your best odds of survival are if you use bear spray, a super powerful pepper spray. The second best thing you can do to improve your survival odds if you encounter an aggressive grizzly is to do nothing, just play dead. Your worst odds of survival by a factor of 12x is to shoot it! Doesn't matter what type of gun was involved, shooting a grizzly is a surefire way to get killed. I know this will surprise you but grizzly bears do not like being shot AND due to their size and slow heart rate, anything other than a perfect shot with a big gun will just upset it and make it die slowly. Source
Bonus content, this is from last year at Great Smokey Mountain National Park. I head someone yell "BEAR" and did what any normal person would do and ran to see it! 😄 Turned out it was a bear cub and no momma bear in site... as soon as I realized that I followed procedure and just started moving away.