What is the difference between microeconomics money and macroeconomics money? In microeconomics, \$USD are a store of value.  I can sell a candy bar for \$1, and I can hang onto that \$1 for a year and then buy the same candy bar for that same \$1.  If I print \$1 (and get away with it), I can wait a year and buy a candy bar with it.  My \$1 has some inherent value.

In macroeconomics, \$USD are simply a means to inject liquidity into the market.  If the world sets up a global savings fund, and puts \$1 into it, that money is moot.  There won't be more candy bars next year than there are this year.  The \$1 is just a means to make my exchange of candy bars convenient.  It has no inherent value.

This is something of an over-simplification, and I'm no economist, so probably not entirely correct.  However, I frequently encounter people who apply personal-finance microeconomics-style reasoning to discussions of goverment fiscal policy.  I have found it to be incredibly difficult to introduce the above distinction, and I have no citations or sources.  This is just how it makes sense to me, and my words are apparently insufficient.

So, does this distinction have a name?  Is this distinction studied in any text and/or academic circles?  What are some ways that the microeconomic dollar and the macroeconomic dollar are two different beasts?  What are some simple ways to introduce this distinction to laypeople?
There is no distinction between money in microeconomics or macroeconomics. In both fields money is  medium of exchange, unit of account and store of value.

The misconception you have probably arises from the role money plays in microeconomics and macroeconomics.

In microeconomics money is almost always neutral - that is it has no impact on the real variables like equilibrium output, labor supply, demand etc. Many micro models even assume money away and prices are simply given relative to some numeraire good. There are exceptions of course.

In macroeconomics money is also assumed to be neutral in the long run but not in the short run. Hence in macroeconomics money is analyzed explicitly by including price levels, inflation etc. For example, as you mentioned one of the special effects of money is that it can provide much needed liquidity that can boost aggregate demand.

If you are looking into name for the distinction between cases where money matter and when not, that is when it is not neutral and when it is (both in micro and macro) the name is classical dichotomy although the concept is again mainly used in macro since in micro money is almost always neutral