Both Energy Accounting and Utility Accounting represent a systematic way of recording, analyzing, and reporting energy and other utility costs and usage on a regular basis. Originally, software for this purpose tended to track only energy services (which can be converted to "British Thermal Units") such as electricity, natural gas, propane, oil, etc. As a result, it was called Energy Accounting software. As software has evolved and "non-energy" utility services such as water, sewer, and garbage were added, the software and the process became known by the broader term "Utility Accounting".
The Utility Manager (for your network) and The Energy Center (100% web-based) software are full-featured utility accounting packages that have development roots back to 1984 - more than 34 years now - and include both energy and "non-energy" services types.