They belong to the person who created the images, ie the photographer, unless the photographer has a contract of employment with the person requesting the images which stipulates that the employer retains copyright.

I'm surprised to learn that anyone would buy another person a 'fairly expensive camera' in exchange for designing a website without some kind of document being created, outlining the terms of the agreement.

The question of camera ownership isn't relevant to the copyright issue - that is automatically vested in the photographer, as the others have confirmed. Ownership of the camera is something they have to sort out between them.

Has the matter of copyright cropped up, or are you just gathering information, in case it does?

This man obviously isn't a professional photographer - if he was he wouldn't be doing deals to get a camera. He doesn't sound much like a professional site designer either if he published a link to an inappropriate site without prior permission. I'm asking because there may be a way the client can assert a copyright over the images. Tell me exactly what is going to happen - you've alluded to the fact that a parting of the ways is possible, is this a certainty, or just a possibility?

Presumably the site is now online - do the clients have access to the server files, and is the domain name registered to them or to him?