That is a great question and it has been addressed accurately by the previous answers. I would like to add that it is interesting that Romanticism would actually be the opposite of romance in the modern sense. When you read a modern romance novel you see a lot of exaggeration, and utter rubbish. The language might be overworked, the characters described quite superficially, and the purpose of romance modern novels is mainly to purely entertain.
The Romantics of the Romantic movement had a different purpose: They wanted to break with the superficial, and indulge in accepting nature and pure character as two very beautiful things, no matter if they were not aesthetically "pretty".
If you think about it, Frankenstein, The Hunchback of Notre Dame, and novels of this sort are considered part of the Romantic movement. Even with their deformed and disgusting characters, what they try to do is to convey the beauty of life, and the charm of existence. They explore the essence of the self, and not the qualities of outer beauty. This is what makes the biggest difference.
I think that the notion of Romance, as thought of in the modern sense, could have some application of Romanticism, but in the final analysis, the ideas are vastly different. The Romantic movement was driven by a desire to laud subjectivity and the notion of personal experience as being critically important to how an individual perceives their state of being in the world. This manifested itself in the idea of believing in the authenticity of emotions and being able to articulate one's own sense of personal distinction. Certainly, Romantic love was a part of this equation because Romantic thinkers admired the idea that love, in its most basic sense, was irrational and could not be explained through logic or reason. It had to be felt. Being enamored with love might not have been the primary drive behind Romantic thinkers- although Lord Byron might have said something different here- but it can be considered to be an implication of the Romantic notion of being in the world.
This literary movement had to do with fantasy or imaginative literature. It is predominantly fiction. In fact, most Romantic literature is larger than life, impossibilities.
In current literature and film, you see the Twilight series, Avatar, Star Trek, Star Wars... People can't grow some of the strange features characters in those films and stories possess. Romantic literature can be science fiction or even historical fiction.
The romance novel of today is a result of some of this "fantasy" writing because many of those situations are highly unlikely to happen in real life.
However, the word romantic or romanticism when in reference to literature has absolutely nothing to do with sexuality.
In short, no, Romanticism doesn't have anything to do with the word, romance, the way we use it today.
Romanticism is a literary movement, marked by rebellion against the neoclassical, the Enlightenment, and the Age of Reason. Romanticism was popular from around 1798 to the 1830's, most specifically, in Britain. The term itself comes from Rome, or Roman.
Romanticism involves an emphasis on intuition, imagination, the personal, rebellion. It harkens back, most specifically, to medieval literature.
i think dat now a days v r not aplying dat idea for our self not any provoking thinking dat results