Are special degrees just an advertisement? My university offers some special degrees; for example


Bachelor of Engineering (Scholar) (Honors)
Bachelor of Mathematics Advanced


If you want to get into any of these degrees, you will need to have an Australian Tertiary Admission Rank of 95 or above.

The normal version of these degrees are


Bachelor of Engineering (Honors)
Bachelor of Mathematics 


If you want to get into any of these normal degrees, you will need to have an Australian Tertiary Admission Rank of 80 or above.

From my comparison both the special and normal degrees are the same with the exception that the special degrees have one or two subjects where students have chances of doing undergraduate research and other benefits:


Access to a wider range of subjects
$500 study grants to buy textbooks each year for the minimum duration of the degree
Being paid as research assistants in summer


Are the special degrees just an advertisement? What difference would doing a Bachelor of Engineering (Scholar) (Honors) make when you apply for PhD in USA? Will the admission committee really care if you did this degree or just a normal degree?
I will answer this part of the question:  "when you apply for PhD in USA?"

Faculty in the USA know very little about Australian degrees and Australian universities.  They will only appreciate the difference between degrees if you explain it to them in your application.  

To be eligible for an American PhD program, someone with an Australian Bachelors will need an honours or a masters, because three year degrees are not sufficient.  Expect to need to explain what an honours is, and that it is not like a UK honours.