There is a list of differences in civ5 difficulties here: http://www.civfanatics.com/civ5/difficulties
What does "Production Free Units" row mean?
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Production free units is NOT the number of units you can have without maintenance. It is the max number of units you can support without suffering a production penalty in all your cities. This production penalty rarely kicks in unless players build giant armies so many people are unaware that it exists, mostly because maintaining a big enough army is too expensive due to the exponential costs. For each unit over that limit you lose 10 percent production to a maximum of 70 percent. You can see this penalty in the top UI bar if it triggers as a -10
The calculation for unit cap is based on difficulty, which is what you are seeing. Max units without penalty is equal to Production free base units + (production free units per city * number of cities) + number of citizens. So on deity it is 5 units, plus 2 per city, plus 1 per citizen.