MMT abandons the use of interest rates and sets the rate at an arbitrary level, usually taken to be zero to avoid redistributing money to savers. Broadly are two crude levers of macro control are monetary policy and fiscal policy and even more broadly, Monetarism is the abandonment of fiscal policy, MMT is the abandonment of monetary policy and Keynesianism is the use of both.
Unless my understanding of MMT is out of date.
Mostly I am using it as easier than writing Keynesianism or Keynesian Economics.
ISLM is the original core idea of Keynes and is explained
here. New Keynesianism has moved beyond ISLM but it's still a useful tool for understanding and explaining Keynesian ideas to a general audience, especially over the last 10 years when the economy has been operating in such extreme edge cases. Krugman has basically built his rise from obscure blogger to NYT columnist on the use of ISLM to explain a leftist perspective on macro to a lay audience.
Beyond that Keynes gets complicated and into ideas like prices being downwardly sticky, long run vs short run, philips curves, etc. There is a good, and readable, explanation of Keynes and Keynes vs Moneterism here :
https://www.econlib.org/library/Enc/KeynesianEconomics.html
Keynesianism is MMT (again broadly) when interest rates are zero or approaching zero because monetary policy stops working and this is the era we have been living through since 2008. When the economy is operating normally, Keynesians believe that interest rates can be used to influence aggregate demand by encouraging people to either spend or save; MMT rejects this or at least sees no need for it.
For the last 10+ years Keynesianism (or at least the progressive end) has advocated expansive spending roughly in line with MMT because the top priority is to restore the use of all productive capacity of the economy and there is no need to worry about deficits or inflation. Indeed the point of the public and academic debate has been the Keynesian view that inflation and interest rate rises are impossible when the economy is in this state and the monetarist argument about hyper-inflation, punishing interest rates, debased currencies etc. (Spoiler: the Keynesians were right).
What happens as when the economy gets back to normal is the big debate in macro economics currently. Specifically, its a debate between different types of Keynesians and concerns things like secular stagnation, the limits of fiscal power both at the zero bound (GFC) and under more normal circumstances (Japan, etc). This is mostly a debate in academic circles although it leaks into public policy debate via people like Krugman and because of the oddly high profile of economics in public debate following the GFC and COVID.
MMT argues that we don't need to change our fiscal policy as the economy returns to normal and can carry on spending until we reach the limit set by inflation. Keynesians argue that this is either the same as Keynes (i.e. you would end up with the same level of spending and we are just arguing about accounting) or that would in practice end up being inflationary because of a lack of political self control and the effective abandonment of monetary policy as a mechanism to control inflation in an overheating economy.
And if you do that you basically get this :
https://worthwhile.typepad.com/wort...011/04/reverse-engineering-the-mmt-model.html