I've worked as a manga inspired/influenced/style artist for years. Although a large percentage of people I meet don't really know what manga is! Let alone understanding the differences between it an anime. Older relatives, or those completely removed from popular culture often need educating. For most people who are unfamiliar, I'll usually just say I draw "Japanese style comics and cartoons". However, I don't think the answer to "What is manga?" or "What is anime?" is a simple 'one description fits all scenarios' sentence. With a little help from Wikipedia I thought I'd try my best at summing it up these definitions.
What is the difference between Anime and Manga?
Anime is a term to describe animation created in Japan. In the west, the term is “anime” is defined as a style and genre of animation typically originating in Japan, and can often feature detailed, colourful imagery, unique, in-depth characters and action orientated plot lines either set in the past, present, future or often within a fantasy setting. The meaning of the term ‘anime’ can sometimes vary depending on the context it’s used in.
Manga is a term to describe comics created in Japan, or produced by Japanese Manga Ka (artists), primarily for a Japanese audience. The style was developed in Japan though the mid to late 19th century with heavy influenced from western and American comics combined with the long and complex history of Japanese art and wood-block prints. In the western world, the term is often defined as a style of drawing originating in Japan and many western artists have adopted this style and refer to themselves as Manga artists.
So we could summarize:
Anime = animation in a typical Japanese cartoon style. Often in full Colour.
Manga = comics in a typical Japanese cartoon style. Often in black & white and with grey tones.