Difference between . and : in Lua

For definition it is exactly the same as specifying self manually - it will even produce same bytecode on compilation. I.e. function object:method(arg1, arg2) is same as function object.method(self, arg1, arg2).

On use : is almost the same as . - a special kind of call will be used internally to make sure object and any possible side-effects of calculations/access are calculated only once. Calling object:method(arg1, arg2) is otherwise same as object.method(object, arg1, arg2).

The colon is for implementing methods that pass self as the first parameter. So x:bar(3,4)should be the same as x.bar(x,3,4).

To be completely precise, obj:method(1, 2, 3) is the same as

do
  local _obj = obj
  _obj.method(_obj, 1, 2, 3)
end

Why the local variable? Because, as many have pointed out, obj:method() only indexes _ENV once to get obj. This normally just important when considering speed, but consider this situation:

local tab do
  local obj_local = { method = function(self, n) print n end }
  tab = setmetatable({}, {__index = function(idx)
    print "Accessing "..idx
    if idx=="obj" then return obj_local end
  end})
end
tab.obj.method(tab.obj, 20)
--> Accessing obj
--> Accessing obj
--> 20
tab.obj:method(10)
--> Accessing obj
--> 10

Now imagine the __index metamethod did more than just printing something. Imagine it increased a counter, logged something to a file or deleted a random user from your database. There's a big difference between doing that twice or only once. In this case, there's a clear difference between obj.method(obj, etc) and obj:method(etc).