One is a spacial measurement while the other is an intellectual measurement. Unfortunately for the OP, these are not the only meanings for these three words in these two two word phrases. The true meaning of almost any two word phrase can only be revealed in its use in a complete sentence.
Jimmy's continued use of the advanced metering LXI protocol instead of the old standard of GPIB IEEE 488 made several programing engineers unhappy since their coding now needed to be redeveloped.
Even though Bob's smart metering approach of including uncertainty values for every measurement meant much more work, the end result proved that Bob knew what he was doing.
Clearly one can substitute the two phrases in the above sentences and not change the meaning of either sentence.
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"Don't disturb my circles." translation of Archimedes last words
With no context provided for these common currently used 'buzzwords' I would say they (generally) mean the same thing, depending on what country you are in and what group is mentioning them.
Another example would be NGR (Neutral Grounding Resistor) and NER (Neutral Earthing resistor). The same thing but two different names depending on what country you are in.
I should add some context. The terms are often used in the UK with regard to 'Smart' being residential and SME customer sites, and 'Advanced' being applied to metering for customers in the profile classes immediately above ie profile classes 5 to 8. The question is what functionality needs to exist in an advanced meter to allow it to be used for this class of site? I believe the 'Advanced' meters comply to Code of Practice COP 5 or COP 10.