The entire idea of Brahma, Vishnu, and Shiva is really rare in Hindu scripture. It came into encyclopedias because the writers of encyclopedias came from the western paradigm. They were looking for parallels, much like you do. They were specifically looking for something resembling the Trinity in Christianity, and stumbles upon the Trimurthi in some vague place in Hinduism. The only thing in common is the first syllable 'tri' meaning 3. Other than that, there is no parallel. I would advise against reading encyclopedias about Hinduism because they get it all wrong. They didn't consult Hindus at all, and just make stuff up that suits their preconceived notions.
To answer your question, they are all names of God, although Brahma isn't worshiped these days. Shiva and Vishnu are both names of God, and are God to Hindus. Those that call God Vishnu are called Vaishnavite, and those that call God Shiva are Shaivite.
Non Hindus see them as representing Creation, Preservation, and Destruction. We Hindus see it as extension, sustaining, and dissolution. So the translation is poor, again, to suit the ideas of the translator. In the reality of the Hindu world, each God would have all 3 of these powers, (because its actually the same God) or acts and more. In Saivism, for example, Nataraja's Drum is for creation, the ring of fire is dissolution, and is upright right hand is for sustaining. He has two more acts, or graces called revealing grace, and concealing grace.
Brahma and Brahman are two entirely different things.
Much better than any encyclopedia or wikipedia is this site:
Hindupedia, the Hindu Encyclopedia It is at least written by Hindus.