I've decided to focus on demisexuality because it's such a controversial orientation/inclination/thing, and really brings the subtleties of the language describing sexual and romantic orientations into focus. Much of this post will be personal - and talk about my own journey with finding words to describe how I tick - so please don't expect too much academic rigour here.
As I've explained in the past - a big part of what being on the asexual spectrum is about (for many people anyway) is some form of disconnect between sexual and affectional ("romantic") orientations. What does this mean, exactly? Ahhhh, let's take a look at the following picture...
When I first saw this picture - I must have stared at it for a good half hour. And then eventually it hit me: I've never been directly sexually attracted to anyone!
Language: Affectional vs Sexual Orientations
It's probably very hard to relate to if you're a reasonably mainstream sexual person who is oriented towards a certain gender, but affectional and sexual orientations can actually be completely separate things. Certain rare people even have separate sexual and affectional orientations for different genders, while for most people on the ace spectrum - it's usually more just a case of them having an affectional orientation - while their sexual orientation is weak, missing, or highly abstract (as is the case with demisexuals).
What affectional orientation sans sexual orientation means is, essentially, that you might find people of a certain gender cute and attractive and you develop crushes on them and "fall in love" with them, but it's not a sexual thing for you. For most people the two aspects of attraction run together so closely that there isn't any need to think of them as separate things - while for some of us they're distinct enough that they require separate attention.
Language Difficulty 1: "Romantic"
I don't particularly like the term "romantic" when talking about affectional orientations. The problem is that it tends to conjure up the mainstream image of what "romance" means to most people - which is almost always a sexual pair-bonding thing. I like the term "affectional orientation" because it's slightly more exotic, and people who are new to the terminology of asexuality usually need to look it up and check up on what it's about - while "romantic" causes confusion because it comes with a lot more cultural baggage.
Indeed, in my case "affectional" feels particularly poignant, because really this is all that my upfront attraction to any new girl can be about - desire for intellectual, emotional, and later sensual affection. Nothing beyond affectionate contact such as cuddling, in the physical realm of things. Not for a long time anyway.
Language Difficulty 2: "Demi-"
The word demi means "half". Some people think it's misleading because it implies that demisexuals have an "incomplete" sexuality, but I actually don't mind the term too much.
Although it doesn't quite describe the dynamic of how demisexuality works, it does sort of embody the point that demisexuals can be either asexual or sexual, depending on the relationship context that they're in at any given time.
For me personally, this is exactly how it is: between relationships I'm as good as asexual. Right now, there is literally not a single person on the face of this entire planet who I'm realistically interested in having sex with. But when I'm in the right emotional headspace with someone in a relationship, I can become essentially no different to anyone else in a standard sexual relationship. So it's like my "sex life" is potentially dominated by either asexuality or sexuality, half-half.
In Defence of Demisexuality
Finally, I'll address the controversy: is demisexuality really a necessary label? Or is it overkill? And are we heteroromantic demisexuals just "normal" - albeit somewhat sexually conservative, heterosexuals - and being special snowflakes demanding attention with this label?
To some degree, I can actually see both sides of this. And as I've explained in previous posts regarding my "label fatigue", I do sometimes wish it was all unnecessary.
But then again, this is what language is all about. Different groups have different specific words for highly specific nitpicky things that have meaning for them (eg. Apparently some Australian Aboriginal languages have dozens of words for different types of tree bark, because it was such an important material for them). There is nothing wrong with words sometimes seeming too specific out of the context of a given in-group, as long as they are useful within the in-group. Or to get a certain point across to outsiders, or to the world at large.
So is demisexuality a unique orientation? Or "just" an inclination? It doesn't really matter to me. I'm happy to just say it's a thing - and as long as it's ever useful to communicate something and avoid potential misunderstandings in relationships, it was a useful piece of language.