they generally use an internal collet that when you push on the top end grabs the lead and pushes it a bit out the end, then lets go as you stop pushing, and retreats back ready for the next push, thus 'propelling' the lead 'mechanically' (some use a related screw mechanism). us americans chose the latter term, the brits the former. one of the joys of english anomalies - gasoline/petrol, car boot/trunk, car windscreen/windshield, lift.elevator, tube/subway, and so on infinitum. not even counting guest words adopted from other languages.
they originally used a lead (chemical symbol Pb - levar?) wire, that's why in english we call the central graphite that does the writing the 'pencil lead'.
luckily they figured out that graphite worked better and left a darker lettering, and later found it was safer. bit more fragile, tho chewing on your pencil is a lot healthier. wears out faster tho. if you have one with a real lead centre, don't use it.
romans used lead for plumbing pipes, the exposure level from it in alkaline water is low, but cumulative, they think rome declined in part from the side effects which includes reduced intelligence, reduced fertility, mental issues, strength, etc.