integer

Integers are numbers with no fractional part. A number can be considered as an integer as soon as it does not have the period decimal separator.

local a = 10 -- integer (can also be considered as a number)
local b = 10.5 -- number only 
local c = 10.0 -- number only, even if the fractional part is equal to 0

You can convert numbers with a fractional part equal to 0 into integers by using the standard function math.tointeger.

local a = math.tointeger(10) -- 10, conversion successful
local b1 = math.tointeger(10.5) -- nil, conversion fails
local b2 = math.tointeger(math.floor(10.5 + 0.5)) -- 11, converted from 11.0
local c = math.tointeger(10.0) -- 10, conversion successful