I am trying to imagine what a solar water heater would look like. Are there different styles for different applications? How would one choose? Would it matter if one were totally off grid?

There are different types of solar water heaters. The differences are mostly dependent on the climate you are in. For most people in most places the collectors are typically 4' x 8' x 4" aluminum boxes that have a glass front and are mounted on a roof or on a rack. This style has proven itself over a long time to be most efficient and cost effective. You can do a web search and see lots of examples. I have a whole chapter of my book dedicated to this subject.

Bob