There were more literate times in English-speaking lands when the meaning of words was less mutable than is now the case. Now they evolve with ascending peculiarities in the outcome:
Gallery used to mean a long narrow hallway connecting two opposing or ajacent buildings. Quite often this place had windows on one of the wide fronts with a blank wall opposite it. This sheltered wall, limited the light, and was seen as appropriate for the showing of works of fine art, most often paintings but sometimes sculpture. Paintings in oil and watercolours are reactive in sunlight so this was a reasonable place to show them. Today, any retail space may be described as a gallery but it is as likely to houses automobiles and furniture as it is art.
Art was a Roman concept and that word equated with a skill regulated by rules of procedure. Alternately, a profession, a pursuit, or a business. In medieval times this word was understood as a skill, or ability to perform certain acts following observation, study and accumulated experience. Since artwas seen as a discipline it became engrafted onto scholastic and academic pursuits to describe various branches of book learning., hence the Liberal Arts. Any systematic application of knowledge aimed at producing a product, ie. a craft, was also regarded as an art form, thus we hear of the Industial or Mechanical Arts. Today this word is used in even wider senses and it seems that almost evberyone qualifies as an artist of one sort or other.