Yes. There is definitely a right, and wrong way to connect the plumbing to a water heater. On most modern water heaters, the cold inlet is marked with a blue marker, while the hot outlet is marked with a red marker.
Not sure why blue means cold and red means hot... Possibly because metal tends to glow red when it's hot, and glacial ice is often blue?
Some people get angry when you call a water heater a "hot water heater". The truth is, sometimes the water heater does indeed heat hot water. So to call it a "hot water heater", is not completely incorrect. This is especially true, given the fact that hot is a relative term. As long as the water is hotter than the "cold" water coming in, it can be thought of as hot in comparison to the cold water.
The term "hot water heater" probably came from combining "hot water tank", and "water heater". Which at one point in time, may have been two different parts of the same system. The water heater would heat the water, and then store it in the hot water tank. At some point the heater was combine with the tank itself, and the names naturally combine as well.