But wages absolutely have gone up, just not as much as other things like cost of groceries or housing have risen.

Inflation does not require perfectly equal increases across all categories. Nor does it require it to occur 'quickly' although it certainly can. It is completely possible for some products/services to even come down in price during periods of inflation. The trend/average is what matters.

It's absolutely caused by greed, yes...but it is still inflation, by definition.

Edit: were you thinking of hyperinflation? Because that would explain the 'quickly' part... But it still doesn't require all products/services to increase in price identically.