Well, these two are not equivalent. Decirme is the infinitive "to tell" form, and it could be used as to object of a preposition, like: Favor de decirme. This literally means "Favor to tell me", which doesnt sound right in English, but it sounds right in Spanish. I don't think you can just say "Decirme" by itself and have it make sense.
Digale is a command "tell him". A closer equivalent is "Digame", which is the command form to "tell me". The me and le are the indirect object pronouns. Really, you are meaning "Tell to me (something)". In a command you just add it onto the end of the word. The command form is actually what is called the "subjunctive", which is also used to express doubt, uncertainty or emotion regarding the verb. I guess you could classify giving a command under "doubt", since you are not sure the other person will do it. The subjunctive is formed by taking the first person singular of the verb-- here is it "Digo", then dropping the "o" and adding an "a" for er or ir verbs, and an e for ar verbs. The usual endings go after this additional letter: a, as,a, amos, an; I don't normally use the second person plural so I don't know what that ending is.