Actually in Spanish there is no difference at all between acordarse and recordar. I think I can use both for any of the meanings you mention. The difference is in the structure and the regime. You say "recordar algo", so it's a transitive verb with a direct object, but "acordarse de algo", so the verb needs a prepositional complement introduced by "de".
The only other diference is that "recordar" can also mean "to remind" (making someone remember something). For example: "Esa música me recuerda mi niñez"="That music reminds me of my childhood". You can also put a preposition "a" before "mi niñez", but it's optional ("esa música me recuerda a mi niñez"). "Mi padre me recordó que mañana tengo una cita"="myfather reminded me that I have an appointment tomorrow". "Acordar(se)" cannot be used with that meaning.