Yup, anime means Japanese cartoons. Anime and manga refer to two different forms of media--cartoons and comics--but if you're talking about the style, they can be used mostly interchangably, because anime-style and manga-style are pretty much the same thing (big eyes, small noses, etc).
Also, if you're talking about a particular series, most popular series will be both a manga and an anime. Inu-Yasha started as a manga, and then had an anime made based on it; Neon Genesis Evangelion started as an anime, and had a manga made based on it--etc, etc. So someone may interchangably refer to Inu-Yasha as an anime or a manga. But the two terms do still have different meanings.
And yeah, there is a certain amount of 'hentai', or japanese animated/comic porn. The japanese are very blase about the whole thing. XD But it'll only appear in series that are geared towards it, and most series in your average bookstore are going to be normal. But it's always a good idea to tread carefully. And the internet can definately dredge up the worst of it...you can type in something totally ordinary, and somehow get tentacles and whatnot. Gah.