can be used in the same context in some situations but they do have some nuances, and they don’t fit properly in any situation, one might adjust better than the rest.
To start off, grammatically speaking, both fear and scare can be noun and verb while afraid is the adjective of fear.
Scare is something that element A inflicts on element B per se.
Dogs scare her.
I scared my sister.
They were scared of him
It is to make someone or an animal frightened. It is something the victim suffers from the perpetrator. Scare might also have a slightly visceral connotation, the reason of being so frightened is much more specific and physical, while fear seems to be a somehow less defined feeling of dread, it has a more psychological side to it.
Fear is different, you can’t grammatically use it directly as in ‘I scared someone’ but you definitely can ‘strike fear in someone’s heart’. It is something inspired by someone else (as in a passive way), it is also the abstract concept of fright; the superlative being terror. The difference may become clearer with the following example:
SCARE
I scare you→ I inflicted fright on you.
I am scared→ I am the one who is frightened
FEAR
I fear you→ I am the one frightened/ scared of you
I am feared→ I inspire fright onto others
Fear has a more looming property to it than scare, it is more ominous and permanent, while scare is more related to a swift ephemeral state of mind, more sudden and sharp.
I was scared for a moment. It is not usual to say, ‘I feared for a moment’. The verb scare adjusts better in that context.
On the other hand, afraid is an adjective that can be used in different contexts that are not necessarily related to fright.
I am afraid I can’t help you
It is a polite way (or even sarcastic, depending on how you use it) of saying that you can’t assist them, which does in no way mean that you are scared or that you feel fear.