Romances are stories of relationship. Often there are many relationships involving family, friends, enemies, but essential to being a romance is the primary one is between two lovers. If they are just friends-- no romance. There could be a third making a triangle, but only for awhile, and it should be obvious to the reader which is the desired winner. Romances today can be between two women or two men. What they will not end up is mènage á trois. There must be a primary couple-- hence, no polyamory. Save that for literature, memoirs and erotica.
Romances also must have a happily ever after. The only known exceptions are in series writing where there will be one but, by the end of the series, not before. Romances are built around the complexities of finding 'the' one and then deciding if it can work. They usually end when the couple have decided they are in love and gotten past the barriers-- frankly, before the hard work of relationships begins. ;)
Romances need two main characters whom readers care about. One or both may have flaws in their character, but the reader has to want to see them get it right or else why keep reading! For me at least, a book with a hero who is a bastard until the last chapter, will not make for a satisfying read.
Even more so, it is a lousy life lesson for readers that such men (women too) can be redeemed through love-- which leads to a lot of divorces, abuse, and sometimes violence. Make them both likable with some flaws. A book that shows growth is a plus. In fact, a romance is all about growth in the relationship and in the pair.
Most romances today go between the hero and heroine for points of view. So sometimes the reader gets inside his head; sometimes inside hers. Rarely is a romance seen from outside the two-- as in the writer's perspective. The best romances do not have an omnipotent point of view, and the writer must work to be sure the changing views are clear and not confusing.
A believable barrier/barriers must keep these two from their happily ever and then it has to be believable that they worked it out. The barrier can be outside them-- as in a villain to be overcome, danger to surmount. Yes, a romance is a fantasy but it's grounded in real life.
For romances, happily ever afters are de rigueur-- tragedies are for literary books where their readers dote on misery. Romance is a feel good read at least by the end. A roller coaster ride with ups and downs but security for the reader that their time spent with these characters will be rewarded.
Romances can deal with social issues, have dangerous enemies, a host of complicating factors, but in the end it's about that mysterious thing-- love and why it works or doesn't.
A straight western has its own set of expectations. It is usually told through one point of view, might be two but no jumping around. If it's historical, it must be accurate to the time period. Westerns are not primarily about romance, but there can be one; there often is but it won't be the main issue. The important plot element will be the battle the hero must face to fix what was broken, do the right thing often at a high cost.
A western has a hero, a powerful villain (else how can the hero show his mettle) and finally a reason the hero gets into the conflict which might be a protecting someone, revenge, getting money, saving a ranch, etc.
In every western there is normally at least one and maybe several battles where the possibility of the hero being defeated is very real. He might appear to have been one or more times. No matter how dire or how great the odds, the hero will succeed but that won't happen before he is threatened, beaten or shot. He usually recovers fairly fast and faces the last challenge where he defeats the villain. A really complex western might even have him facing the villain, only to find the real villain is behind the scenes-- one last conflict that the reader and hero didn't expect.
To make a western the most exciting, the hero is facing a psychological and moral dilemma as well as a physical one. Westerns, like romances, are fairy tales to take the reader out of their daily life. They are dream fulfillment books.
So how do you define a western romance? I think it's a mix of the elements in each. There will be a conflict where the heroine might take an equal share in resolving. The hero and heroine will be important parts of the story and most often the point of view goes between them; so we know what each is thinking. They will face a conflict that involves real danger while they are also facing the problem of what to do about their relationship. Both may have ups and downs. A sweet western romance might just be set in the West, involving making a town or community right, but may not have a dastardly villain.
Western romances have the ethos of the western for the good against evil. I think most of them have alpha heroes but that does not mean brutal men. It means the kind of man others turn to in times of turmoil. The heroine will be his equal as she either stands at his side through the battle or fights her own to get to their happily ever after. Generally speaking western romances have action in the story.
Western and western romances end happily.