Usually some muddy thinking.
The old sizing systems referred to the size, the diameter of the complete wheel - inflated tire, on its rim.
Trouble is, the overall diameter varies with the width of the tire, and people tend to replace tires a lot more often than they replace rims.
This means that a bigger wheel with a narrower tire can have the same diameter as a smaller wheel with a wider tire.
It's particularly bad in 26", where there are 4-5 different 26" rim/tire sizes which don't mix with each other.
A much more sensible approach is the ETRTO sizing system, which refers to the diameter where the tire and rim overlap. If the ETRTO number matches, you're at least guaranteed that the tire will be able to mount to the rim.
Now, the story doesn't stop there. Some tires are just too wide or too narrow to be a good choice for that rim. And some tires are too wide to fit a certain frame/fork. But it's still a good deal better than referring to the outer diameter of the rideable wheel.
Tires off the rim, or the tire and rim off the bike?
Kinda-sorta, but it'd depend on how finicky you are, and what bike you're talking about. A "real" road bike will often be built only to take narrow, high-pressure road tires, so a wider, softer terrain tire just won't fit in the frame/fork. But if your bike has enough room for wider tires, then there are "terrain" tires available for most of the wheel sizes used today. The biggest selection is in the 26" AKA 559 mm ETRTO and the 28" AKA 700C AKA 622 mm ETRTO sizes, where you can find tires for just about any terrain. Spiked/studded winter tires, tires for gravel/hardpack, mud tires, and so on.
This is a recumbent exercise bike that is made for indoor usage and you can't put off road tires on this unit.
Aspen is a bike tire made by Maxxis. -Reputed to be very good off-road tires.
vice versa
Bikes styles all have different tires to suit terrain. There are road racing tires, cruising tires, off-road tires and many different wheel sizes too.
A mountain bike is basically a bike meant to be strong enough to be ridden off road. It's overall stronger and has wider tires than other bikes.
It depends on what kind of rider you are. If you ride daily, make sure your tires are properly inflated at all times. This will save on eventual damage to the rims. After a ride, check the tires and rims to make sure that all is in order. If you have a lot of time between rides, store the bike up off the tires to prevent them from getting out of shape, which will hurt the rims. If you are a serious rider, talk to the expert at the bike shop about other suggestions to keep your specific bike in top shape. To get the most life out of your bike tires and rims the best thing to do is keep the tires properly inflated. Properly inflated tires will protect the rims well giving the best useful life for the tire. Checking the condition of the tires and replacing them when they become worn or when you can not repair any damage will help to keep you rims in the best shape.
A street legal dirt bike is any dirt bike that has a four stroke motor, head lights, brake lights, turning signals, a spark arrestor in the silencer, and street legal on-off road tires.
It depends what use the bicycle is put to, it may be a racer, a road going tourer or an off-road mountain or trail bike. All have very different tires.
While riding - usually not unless flatted or busted. if its about if they can be taken off - sure. You need a few tools - tire irons/levers, and a little skill.
When your tires rub against the surface you are riding on to slow you down. When your but is rubbing against your seat to stop you from slipping off. When your hands rub against your handlebars to stop them from slipping off.