Any animation that is not made by a Japanese production company is not anime, according to the English definition of the term.
To Japanese people in Japanese, the Japanese words 「アニメーション」 and 「アニメ」(animeeshon, shortened to anime) are used to describe any animation, whether made in Japan or made in other countries, such as Disney.
It is important to distinguish between the Japanese word used by Japanese in Japan to describe all animation from all countries, as compared to the English word which is distinct from that in meaning. The English word only refers to animation that is made by a Japanese production company. It includes many series which were almost entirely animated in Korea by Koreans, but done so for a Japanese production company. Look in the credits list at the end of many anime TV series and you will see many Korea names; since the company is Japanese, it counts as anime, even if the animating work was largely accomplished by non-Japanese people. If the exact same Korean animators created an animated series produced by a Korean company, it would not be anime according to the English definition of the word.
Korean comics are called manhwa. There are a handful of American publishers that might market a graphic novel to you as "manga made in America," but that is actually an oxymoron. The English word "manga" only refers to comics produced by Japanese publishing companies. Japanese people do not usually use the Japanese word 「漫画」 (manga) to refer to comics from other countries; instead they say 「コミックス」 (komikkusu). Again, you could be a non-Japanese living in Japan and having your comic published in a Japanese manga magazine, and it would be real manga, because of the company, regardless of your own ethnicity. But if you are ethnically-Japanese publishing your comic outside of Japan, it is not manga.
Another important thing to keep in mind is that neither the English word nor the Japanese word contain anything related to art style. This is also true of words such as shounen, shoujo, seinen, josei, and so on: within each, there is a wide variety of art styles. For example, compare the art style of Kaitou St. Tail to NANA, to Kiko-chan Smile, to Ace wo Nerae, to Zetsuai 1989. They are all shoujo, but they do not look alike, and there are respective shounen series that look more like one of them than the other.
Shounen, shoujo, seinen, and josei are words that can only be used to refer to sub-genres within Japanese comics and animation; they cannot be applied to animation produced in America or any other countries. Rather than genres proper, they are simply technical groupings of marketing targets: was this series targeted at young adult women, or not? You can promptly tell which type it is by which area of the Japanese bookstore the manga is in.
According to Energetic Heartbeats,
What is Shoujo?
Shoujo (girls') is not a genre itself - it's the marketing strategy. Shoujo simply means that the title was originally marketed to a female audience in Japan. Nothing more than that.
Shoujo includes its own genres that cannot be found in their original form within the shounen world, including mahou shoujo, shounen ai, yaoi, yuri, and others.
Shoujo is not limited to only anime and manga. The word is also used for audio dramas and novels. . . . Pretty much any film genre you can think of has been represented in shoujo.
What is Not Shoujo?
Shoujo is NOT a type of art style, nor a type of story element. It is not even neccessarily work by a specific creator. For example, the beloved team CLAMP is responsible for outstanding examples of shoujo manga and anime, but has also created shounen manga. What's the difference between the shounen manga and the shoujo manga? The shounen series was serialized in a manga magazine aimed at male readers.
