What is the difference between microeconomics money and macroeconomics money?
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