The elements captured in Impression, soleil levant are precisely what a photographer might hope to capture, the reflections and colors of the landscape. Impressionism was a phase than many artists of the time went through, they gave it a go and then gave it up when it bored them. For Monet, Impressionism was his only style, the way in which he saw the world.
The ideas which drove the work of the impressionists are also found the the thoughts of contemporary philosophers. Frederic Nietzsche said "Art is not merely an imitation of the reality of nature, but in truth a metaphysical supplement to the reality of nature, placed alongside thereof for its conquest." Art became how man viewed nature, or how he cared to mold it.
An article on the ideas of Impressionistic Aesthetics can be accessed at JSTOR here. The ideas seen in painting also carried over into the other art forms. Debussy was considered by many to be the leader of musical Impressionism, though he continually denied the title. He didn't believe that his music followed Impressionism, but it seems that he merely wanted to claim distinctness.
Like his contemporary artists, Debussy was influenced by the import of Asian traditions and rejected traditional European formulas saying "There is no theory. You have merely to listen. Pleasure is the law." As painters were titling their work in musical fashion, Debussy was creating musical interpretations of visual experiences. The following piece in entitled "Voiles" or "Sails."
Post-Impressionism emerged as many artists tired of Impressionism, and has no cohesive definition of criteria for inclusion. This movement is primarily made of painters who exhibit a strong Impressionist influence, but have departed from the practice. Paul Cézanne is considered among the best examples of this period. He also pushed the transition from naturalism to abstraction as we can see by comparing two paintings of the same subject, but from different points in Cézanne's career. First from 1868 and then from 1902:
Cézanne isn't striving to capture the light of the moment as was Monet, but rather use strokes of color to represent his subject. The rules of academic painting were further suspended by Cézanne and other painters followed suite. Symbolists painted what they felt and imagined, what they subjectively believed about the world. The only moralizing now came from the artists' personal codes rather than what was dictated for the collective. Gauguin painted his most intimate feelings in Where Do We Come From? What Are We? Where Are We Going? instead of depicting an actual observed scene.
These movements, Impressionism, Post-Impressionism, and Symbolism are best understood in terms of each other and how each was born of the previous.