"Vegan" is a popular term in everyday language, while "plant-based" often appears in scientific literature. Is there any difference in meaning between the two terms?
The term vegan was intended by those who coined it to encompass lifestyles that respect non-human animals and refrain from any exploitation of them.
Although the vegan diet was defined early on it was as late as 1949 before Leslie J Cross pointed out that the society lacked a definition of veganism and he suggested “[t]he principle of the emancipation of animals from exploitation by man”.This is later clarified as “to seek an end to the use of animals by man for food, commodities, work, hunting, vivisection, and by all other uses involving exploitation of animal life by man”.
This has been updated to use more inclusive phrasing - the Vegan Society [now gives] this definition:
Veganism is a philosophy and way of living which seeks to exclude—as far as is possible and practicable—all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, humans and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals.
This definition clearly implies a philosophical stance against the exploitation of animals.
The term "plant-based" lacks this specific association with an ethical stance, but simply describes a diet or product that is entirely or primarily composed of plant-derived elements. I'm not sure what scientific contexts you are referring to, but considering, for example, the participants in a study, one may describe a group as following a plant-based diet without the implication that they were doing so due to a particular ethical belief.
As a shopper, I would have expected a description including the term "plant-based" to mean that the product is vegan, but unfortunately this may not be the case, as the legal definition for "plant-based" may allow some amount of dairy, egg or honey to be present.
Grateful thanks to Michael Altfied for helping to make this answer way better by pointing out to me that the Vegan Society's definition of veganism has been updated and that the definition of plant-based may include some animal products!