If you have been consuming anime and manga for a while, this might seem like a question with an obvious answer—however, this is an extremely reasonable question to ask! When I was first getting into anime, I personally had no idea and thought (for a while) that “shonen” (i.e. male-oriented content) was manga whereas “shojo” (i.e. female-oriented content) was anime, simply because they had very different art styles and I didn’t know what the terms meant. However, the real answer is quite different and rather simple.
“Anime” is animated television or movies, whereas “manga” is comics written on a page; that’s it. Both anime and manga can encompass any genre and address any theme, although they do sometimes tend to fall along thematic and genre lines that are unique to and popular in anime, such as “magical girl” or “mecha” anime. Oftentimes, but not always, anime series will be adaptations of popular manga series. The same way directors often adapt popular books to film, manga is often adapted into anime because the original media has already built a fanbase and also has established a plot, art style, and set of characters, so the director of the anime does not have to do that themselves (and thus their job is easier.)
Both anime and manga are differentiated from western media by virtue of having very distinct art styles and sensibilities from western comics and animation. They have their own tropes, traditions, character types, and cultural language that is nearly untranslatable to other forms of media. Overall, it is easy and correct to think about anime and manga as the same general cultural product delivered in different formats, even if a given anime might not actually be an adaptation of a manga. With very few exceptions, they share the same basis, worldview, cultural tropes, and stylistic choices.
If you’re interested in both anime and manga—the art style common between the two, for example, is something that draws new fans in—but don’t know where to start, there’s no right answer to that question. It may be slightly easier, however, for someone to begin jumping into both by watching anime because manga is typically written right-to-left rather than left-to-right, which can be a disorienting experience for a first-time reader. Also, anime usually has short episodes, about 20 minutes long, which makes for an easy starting point for a new consumer. Also, anime can either be watched “subbed”—i.e. with subtitles—or “dubbed”—i.e. dubbed with English voice actors, depending on your personal preferences.
All in all, there is no right way to get into anime or manga, but it’s important to know the difference! With that knowledge, it will be easier for you to parse through conversations and information you might hear about both to best understand the genre.