Generally, people know only one of the two famous James brothers. Literary people know Henry James; psychologists, philosophers, and religion scholars know William James. I've often encountered people who knew a great deal about one brother, without realizing he was related to the other.
Henry James pretty much always knew he wanted to be a writer. A quiet boy more inclined to observe and record "impressions," he was remembered by his family for always scribbling away at stories that did not impress them at first. Nevertheless, Henry James found quick success as a writer, and produced a vast corpus of stories, novels, criticism, and travel writing. He was younger than his brother, but achieved fame much earlier. He is sometimes regarded as the writer who turned storytelling into a true art.
William James had a much more circuitous route to fame. He was far more outgoing as a boy, and is remembered for having had a hard time deciding on a career path. Even after he gave up on a career as an artist, he found himself pulled between a range of interests. He wound up doing a little of everything. He helped found the science of psychology, he launched the philosophy of Pragmatism, he wrote a seminal book in the study of comparative religions, and much more. He is now more obscure than his brother, but his influence touched a broader range of fields and disciplines.
Their correspondence reveals mutual inspiration. William and Henry James served as each other's muse and critic.