I generally try to avoid using the word “acceptance” in my everyday clinical work. I found that people can become resistant when I say “accept it”, normally when I follow it with “allow it to be, let it be, without struggling”, they immediately get it, or at least become more “accepting” to the idea of acceptance.
Acceptance is not wanting or liking. You accept how things are going for you, doesn’t mean you like or want things that way. I accept that my cat has to be put down due to lymphoma, doesn’t mean I like or want him to be put down. I accept the sadness that comes with the loss, doesn’t mean I like or want to be sad.
Acceptance is also not tolerating. They are very different, do you want people to accept you, or tolerate you?
Acceptance is more about allowing things to be that way, accommodating it without struggling (so much) with it. Normally it applies to things that you can’t change directly (external events which you have no control on, e.g. your cat has lymphoma; but also includes your internal thoughts and emotions, which you can’t simply chuck away like a piece of paper, e.g. sadness, fear, anxiety, thought of “I’m not good enough”).