It's just because cigars (and presumably pipes?) are puffed, not inhaled. You absorb nicotine through the mucus membrane in your mouth (not as much), and otherwise enjoy the flavor. The practice with cigarettes is to inhale into your lungs. You could technically puff a cigarette I guess.

People make a big deal out additives and accelerants, but the carcinogens are 99% from smoke, burning plant matter. In that respect, pure tobacco isn't meaningfully safer. That said if you "puff", that's probably safer, though still risky (mouth cancer, and you're still going to inhale some amount of smoke).

A common assumption. A filter filters out harmful stuff right?

Except they don't:

https://exposetobacco.org/wp-content/uploads/Cigarette-Filte...

There have been calls in the Netherlands (perhaps even at the EU level) to ban filtered cigarettes, for the simple reason that they are misleading and offer no protection, but are harmful to the environment because of the non-degradable micro-plastics.