acordarse vs recordar
Both mean 'to remember' — acordarse is reflexive and personal, recordar can also mean to remind.
acordarse
To remember (reflexive) — the memory comes to you, often as a task or something important.
¿Te has acordado de llamarle?
Did you remember to call him?
Remembering to do something. Acordarse de + infinitive is very common for this.
No me acuerdo de su nombre.
I can't remember his name.
The name isn't coming to you. Reflexive construction — the forgetting is happening to you.
Me acuerdo de cuando éramos jóvenes.
I remember when we were young.
Nostalgic recall. Acordarse de + noun/clause.
recordar
To remember OR to remind someone — can be transitive with a direct object.
Recuerdo perfectamente ese día.
I remember that day perfectly.
Direct object — the memory is a thing you hold. More deliberate than acordarse.
Recuérdame que llame al médico.
Remind me to call the doctor.
Recordar = to remind. Acordarme can't do this. Key difference.
Me recuerda a mi abuela.
It reminds me of my grandmother.
Recordar a = to remind someone of something. Very useful, often missed.
Tricky bit
'Recuérdame' = remind me (you tell someone else to prompt you). 'Recuérdalo tú' = you remember it / remind him. Acordarse can't function as 'remind' — only recordar has that power.