It’s hard to give an ELI5 answer, because that difference is somewhat the whole point of Keynesian economics. Moreover, “Keynesian” can mean a lot of different things–what Keynes said, the historical Keynesian school, Post-Keynesians, Neo-Keynesians, and I’m probably missing some. And of these, the Neo-Keynesian flavor is the only one somewhat consistently taught in economics programs.
My stab at it: full employment is always “all people who are willing to work at the current market salary have a job”, the difference is whether or not the market gets there on its own.
In classical economics, anyone who wants a job at the current market salary can get one. If anyone doesn’t have a job, it’s because they don’t want to work at the current market salary (i.e. they are voluntarily unemployed).
Keynes went “dude, just take a look out there, people can’t find jobs and that’s not because they’re too greedy or lazy”. His theory is that demand drives the economy and therefore full employment often requires that the government boosts the demand; otherwise, you have involuntary unemployment.
In classical economics full employment is a long run equilibrium between supply and demand and is basically independent of policy.
Keynesian full employment is the level of employment where additional demand side measure (ie the government buying stuff) will drive up prices but not employ more people.
Policy wise this is important: Keynes says that the government has a role pushing the economy to full employment, classical theory does not.
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