Yes. Not everyone who got the plague died, although a large percentage did (plague is fatal ~half the time without treatment), and there can be different degrees of spread for a particular plague epidemic.

There are actually three types of Plague, all from the same bacteria. The most common one, Bubonic Plague infects the lymph nodes, but it can be airborne as pneumonic plague as well. The most serious form is septicemic plague, which is the lease common because you generally die within 24 hours of symptoms presenting without massive doses of antibiotics

Some strains of the bacteria aren't as deadly, and some aren't as good at infecting new people. Some are too deadly and kill people very quickly before they can infect a bunch of other people. The Plague bacteria actually still exists today and there are minor outbreaks every now and then even now, although they are extremely rare in countries with widespread access to antibiotics.

there is a difference between the normal one and the one in the lungs (that's 99% lethal).

The intensity depends on two other factors:

1. response of local authorities (which over the course of the centuries became more adept at dealing with outbreaks: one such measure was quarantaining (The Venetians had an island for that), ships using special flags to signal the disease on board, etc. The duke of Milan infamously bricked in any house that had a patient in it: harsh but it worked.

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2. the health of the population: as mentioned before, resistance did improve in the population, HOWEVER: famines (either due to war or bad harvests) impacted the health of the population that was affected by an outbreak.

People get infected by it in the present day.

Antibiotics help a lot, and we didn’t have those in the 1300’s.

Yes. Both intensity of the illness, and intensity of the outbreaks.