Let's start with M1
A category of the money supply that includes all physical money such as coins and currency; it also includes demand deposits, which are checking accounts, and Negotiable Order of Withdrawal (NOW) Accounts.
This is used as a measurement for economists trying to quantify the amount of money in circulation. The M1 is a very liquid measure of the money supply, as it contains cash and assets that can quickly be converted to currency.
M1 is basically spending money -- money we are most likely to use in daily transactions. Also note this definition includes demand deposits, which we access with debit cards -- a far more common transaction these days.
Above is a chart of M1 in logarithmic scale. Notice that it rose consistently from 1975 to the mid-1990s, then moved sideways until just after the recession of the early 2000s. It moved slightly higher again before moving sideways for the second half of the last expansion. During the recession, the Fed pumped a lot of money into the economy which explains the big move higher starting in the middle of the last recession.
The above chart fleshes out the relationship between M1 and GDP by using the scale 100. Notice their is a strong correlation between the two, but the correlation is not exact. In the mid 1990s when the economy continued to grow, M1 was near stagnant. The exact same situation played out in the expansion of the 2000s. The reason the economy continued to expand during both of these sideways moves in M1 was monetary velocity continued to increase:
In the above chart of M1 velocity, notice that velocity continued to increase in the second half of the 1990s and 2000s expansion. As the pace of money moving through the economy increases, lesser amounts of currency is needed.
Above is a comparison of the year over year percentage change in M1 and GDP. Notice there is a general relationship from 1975 - 1985. However, as the year over year rate of change in M1 becomes more extreme in the late 1980s, its relationship to GDP is oddly reversed for the years 1985-1987, although you could also argue there is a delayed effect of the monetary spike.
M1's YOY percent change was also fairly extreme in the 1990s. It bears some relationship to GDP performance, but not enough to warrant any firm conclusions. The same is true for the relationship between M1's YOY and GDP's YOY percentage change during the 2000s
What I find interesting is the one to one correlation exists, but it is not as strong as I would have expected (although the lack of strong correlation for part of the time is explained by higher monetary velocity). I'm also very interested in the YOY charts. It could be argued that flooding the economy with money during and right after a recession has an effect, but the effect is much weaker when the economy is already expanding.