We have seen lots of bears and coyotes (actually a coyote wolf hybrid) and no one denies they exist. I have personally seen a bobcat and we are in its “officially” recognized range, although bobcat sightings hereabouts are rare. There was a report of a mountain lion sighting (by a couple of police responding to a complaint) about a mile from me in 2003, but I think it was actually a bobcat, which is scary enough. There is a lot of undeveloped conservation land around here and several square miles of what was once part of the Army Natick Lab that was contaminated during World War II and been closed to visitors ever since.
One thing I have never seen was cougar. There have been reports of mountain lion sightings in Western Massachusetts repeatedly over the years, but I tended to dismiss them. Now I am not so sure.
They're all cats. The same attributes and instincts and even skull structure of Sylvester black-and-white American shorthair or a nice little tabby, exist in every other cat from bob to couger. Cats are natural stealth critters as well as being pretty smart, so there are probably a lot more bobcats and even cougars than folks suspect.