The real difference (when there is one) is in what the different forms of expression EMPHASIZE.

In particular, if you wish to emphasize that a particular thing should be given to you RATHER than to someone else, you would use the preposition — “Give the money to ME.”

If the emphasis is more on the direct object (the thing being given), or if neither is particularly emphasize you would be more likely to omit “to”.

For example:

emphasizing the object — “Give me the MONEY.”

emphasizing the verb – “GIVE me the money.” (Don’t make me take it from you.)

“Give me that gallon of milk” or “Give me your lunch money, punk”

Give to me… well that’s not actually used too often. One will usually say “Give *blank* to me” wherein blank is an object So for example:

“Give your lunch money to me” or “Give me that gallon of milk”

They’re literally used the same way.

Which means, they both mean the same thing.