There is perhaps a subtle distinction in designating pressures that has not been brought out in this thread. It is almost a point of grammar, rather than engineering, but here goes.
Common "suffixes" in designating pressure are:
"a" - absolute
"g" - gauge
"d" - differential
These suffixes may be, and are, used irrespective of whether the units are US customary, or "metric"/SI.
However, if an increment of pressure is referred to, and it is either outside of any context, or the context is understood (at your own risk of causing a MISunderstanding), the proper term is to simply speak of "psi" of "bar". For example, in a table of conversions, one ought to see something like
1 bar = 14.5 psi
Therefore, both of the examples that you gave to illustrate your confusion are correct "mucour", and "jte" really ought to have written "1 atm = 14.7 psi" and "1 bar = 14.5 psi" without the "a" suffix.
Of course, an exception is the (somewhat bastardized) units of "ata" = 14.223 psia, where "absolute" is part of the definition of the units.
BTW, There should be a similar distinction in talking about temperatures vs. temperature differences. For example to say "the boiling point of water is 212 degrees Fahrenheit at 14.7 psia" and "the steam superheat is 150 Celsius degrees".
In context it is often easily understood, but it is sometimes a useful distinction.