
Unlike visual novels, the gameplay here can be fairly complex. The most familiar example is probably the Tokimeki Memorial series, though there are many other highly successful examples such as Love Plus. These games do feature gameplay, but the object of the gameplay is to get into a romantic relationship with a character from the game.
Dating Sims are a different category of game from Visual Novels. Fate/Stay Night is an example of this style. In English usually people will abbreviate this as NVL, and games where the dialogue is in a box at the bottom of the screen are called ADV.
This distinction is more common among Japanese speakers than English speakers.
Visual novel can also be used in a more technical way to describe games where the text is overlayed over the background as opposed to being presented in dialogue boxes. It would not usually be used to describe eroge which are solely sex scenes. Calling something a visual novel emphasizes the "novel" aspect and suggests that there is at least some semblance of a story.
More on this in the related terms section. A more canonical example would be Higurashi no Naku Koro ni, though purists will sometimes insist on calling it a "Sound Novel" as this is the official description. For example, Danganronpa could qualify as a visual novel, but probably not for any of the other categories here. It may or may not involve any romance or sexual encounters.
Visual Novel (ビジュアルノベル), often shortened to VN, is a general type of game with a lot of dialogue and minimal gameplay (usually the gameplay is reduced to just making choices at a few plot points to determine what route one enters). For example, Kamidori Alchemy Meister is an example of a game without a great deal of visual novel content but which still qualifies as an eroge. This includes some games that are not traditionally included as visual novels or dating sims. Eroge can be any game with sex scenes (also called H-scenes). Clannad), but in English this isn't really a correct use of the term. Native Japanese speakers sometimes use the term to describe games without any sexual content (e.g. Eroge (エロゲ) is a Japanese shortening of "erotic game". In any case, when it isn't important to be precise, these terms are often used interchangeably. However, which word you choose places the emphasis on different aspects of the game.
All of these are closely related and many games would fall into more than one category.