Originally, writing romance was much more clear. You had Christian or Inspirational Romance, which followed Christian Book Guidelines. Then there were the normal romances, and last there was erotica.
Unfortunately, normal romance spanned everything from no onscreen sex to up to five detailed sex scenes. You have a population of people who are not Christian that do not appreciate sex scenes or swearing but who also do not want a Christian element in their romance novels. This led to the development of "Sweet" and "Clean" Romance novels.
First, understand that "Inspirational" and "Christian" romances are synonymous. Christian books have Christian characters. These characters cannot lie without a really good reason, gamble, or drink. No character in the book should swear openly and Christian characters should not swear at all (i.e. you could say "Billy the Kid swore as he saw the sheriff approach" but not print actual swear words). There should be no graphic (i.e. detailed) or even glazed over sex scenes and violence should be minimally described without detail. Pre-marital sex should not happen--especially between Christian characters. In addition, since the characters are Christian, there may be instances of "preachiness." My Series of Inconvenience is an Inspirational/Christian romance series, like the Inconvenient Widow.
"Clean" is currently under attack as a naming system. This is because a lot of people are closed-minded and ignorant. They associate clean with getting in a bathtub. They think if some novels are "clean" than all other novels are "dirty"--purportedly because that is the opposite of "clean." They further argue that they do not read "dirty" novels just because they like sex scenes, since sex is not "dirty." Whether or not "dirty" is a bad word and should not be associated with books containing sex is a silly debate because "clean" also means "virtuous," "righteous," "chaste," and "moral." I am married with five kids. I don't see sex as "dirty," but "clean" is not just about sex. Clean books are just a small step above Christian books in that they have basically all the same rules, except there are no Christian characters, so everyone has to follow the rules of no drugs, on-screen sex, alcohol, etc. Violence should be minimally described. Swearing should be mild or non-existent. On example of my books that would be in this category is The Viscount of La Soutain.
Next, is the "sweet" romance. Here, nothing is detailed or on-screen. The focus is still on emotional attachment as opposed to physical attachment. Swear words are mild--no F-words but maybe a few cr--s. Alcohol might be involved. Pre-marital sex is okay, and they may imply characters have sex (married or not) off screen. The rules are a little more lax, which creates problems. Some sweet romances include descriptive sex scenes--and they shouldn't. This is especially true since we now have "flavors" of regular romance. The Baroness of Surli is an example of a "sweet" romance.
Above these, you have the standard romance categories. I don't edit or write sex scenes, so I don't have examples for these:
As we move up the scale, we get to "Warm" romances. These have one described sex scene and nothing kinky. Attraction can be the main or only basis for the relationship. Swearing should be kept to a minimum with "light" swear words. Violence shouldn't be graphic. Everything else, drinking, gambling, etc. is fine.
"Steamy" romances are another rung up the ladder. These have 2-3 described sex scenes--but nothing kinky. Swearing can occur, but shouldn't fill the book. Like above: violence shouldn't be graphic but everything else goes.
"Spicy" romances are the highest level of regular romance novels. These also have only 3-5 sex scenes, and similar guidelines as those as the "steamy" level, but kinky sex (such as BDSM) is allowed. Almost anything goes.
Above all the standard romance categories, is Erotica. Just like "art" vs. "pornography" is often defined by the value of the work, people try to argue their "erotica" should be classified instead as a "spicy" romance because they have written a story that goes along with it. I say that is a dumb measure that Supreme Court Justices used to justify allowing pornography into the mainstream. The true difference in my opinion (which some may argue is not really a difference) is whether the purpose of the work was to sexually arouse the reader (or in the case of pornography, the viewer) or whether it has some other purpose. Poorly written books with descriptive sex scenes are erotica by my standards (and technically the Supreme Court's since there is no literary value) even if they have some semblance of a plot. Erotica is not necessarily one sex scene after the other, but the whole purpose of the book is to get to the next sex scene. The easiest way to discover if you have written erotica is to remove every mention of sex, send it to a beta reader without letting him/her know the book originally contained them, and see if the beta reader likes the story. If it passes the beta reader test, then look at the sex scenes--how many are there? How detailed are they? If you have more than five sex scenes in your book or if those scenes are usually longer than five written pages, you have probably dabbled into erotica even though you have a plot.