"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”.
The language is decidedly dated, and I hope veganism can be defined more inclusively (in terms of gender and as rooted in multiple belief-systems) but I think it would be reasonable to say it is a term implying an ethical stance.
To say that someone is following a plant-based diet is to say they are eating no animal products (presumably without other lifestyle changes). There is no philosophical position or belief system implied behind their practice. This makes it useful for the purpose of reporting on research, where participants may have switched to a particular diet for the purpose of a study. It also includes people who don't eat animals but don't consider themselves vegan.