What is the difference between a local function and a normal function?

[XAXA]

Just to give you an idea:

function foo()
    print("Foo.")
end

is exactly the same as

foo = function()
    print("Foo.")
end

and

local function foo()
    print("Foo.")
end

is exactly the same as

local foo = function()
    print("Foo.")
end

** with a small difference:

What is the difference between a local function and a normal function?

These two specifically are not exactly the same; they have a tiny difference in their scopes. Within the one defined as local function, foo (its name) can be accessed as an upvalue for recursion, while in the local foo = definition, it can not.

The first (function foo()) makes foo a global variable, and the other (local function foo()) makes foo a local variable. With that being said, as with any other variable, you should always declare functions as local.