"No, my dad is not busy today."
Translation:No, mi papá no está ocupado hoy.
Father = padre
Dad = papá
One is more "proper" or "stuffy" and the other is more "relaxed" or "common".
Está is from the verb estar.
Es is from the verb ser.
Both mean "to be", but ser is for inherent characteristics of something, and estar is for conditions.
Es aburrido = He is a boring person.
Está aburrido = He is bored.
Oh my gosh, thank you I couldn't not figure out when to use which one and why!!
I think you're mixing up esta and está.
Esta = this (feminine)
Esto = this (neuter)
Está (with accent mark) = is (needed in the sentence above to say "....my dad is...."
padre is for more formal use. papa is more common. but I get where you are coming from and it should have been accepted