Well it depends in what context, but generally speaking they all take a system approach when evaluating the energy performance of an existing home. The term use for what kind of energy inspection you are getting depends on what inspection protocol the certified professional is performing.
The main drivers of these terminologies have been the power companies. At least here in Georgia for example, it used to be that if you were a Georgia Power customer you would have to get a Home Performance with ENERGY STAR audit in order to qualify for their rebates and incentives programs. Today, they require that you get a BPI assessment. Hence, the general public is getting a bit confuse.
Basically, anyone that says he is a HERS rater means that they are a certified professional under RESNET (Residential Energy Service Network), a Building Analyst would be someone certified by the Building Performance Institute (BPI). These organizations have their own requirements and testing protocols used to address combustion safety and energy efficiency.
Now, if you are planning on qualifying for a Energy Efficient Mortgage (EEM) or Energy Improvement Mortgage (EIM) as a way to finance your home energy improvements projects then you would required a certified HERS rating.
I suggest that prior to engaging on any home energy audit, you first check with your power company for participating contractors, if none are available either go to RESNET or BPI website to find a list of certified professionals in your area that can assist you in your project. Last, if you think you need major energy improvements do not forget to check the Energy Improvement Mortgages.