This can go in both directions, with the stricter meaning being broader, as well as it being narrower. Sometimes it can even overlap.
Meningitis technically means any inflammation of the meninges, but is often used to name any of the several infections that have it as a symptom.
E-mail and email can - and did - mean any of several forms of electronic delivery of messages over a network (whether actually transmitted over the network, or with the messages remaining on one computer shared by several users). Now it almost always only means the form of Internet email most commonly used.
Atheism technically means only a belief that there is no god, but is often taken to mean a disbelief in several other religious ideas.
Overdose means you have taken more than the prescribed dose, even if only trivially, but is often taken to mean a dangerous overdose.
Abortion in relation to a pregnancy technically means an event in which the pregnancy ended before full-term, but is often taken to mean only an induced abortion (and there's a reason why people who don't know medical terms shouldn't read their medical records - I've heard more than once of a woman being upset to read her miscarriage described by the technically correct abortion).
Some come from words being borrowed from other cultures. Tantra technically refers to a range of related styles of religious practice, but in English often refers only to a particular subset (most often those with a sexual component - sex sells).
And many trade-marked items came to refer to rival products. E.g. Hoover is the name of a company, and a trade-mark, but in many places hoover refers to a vacuum cleaner regardless of manufacture, or as a verb to using a vacuum cleaner.