Before answering, in your question, you should change "anonymous" with "synonymous". Anonymous means, without identifying. Synonymous means similar or almost the same. (little hint for you ;-) "Come to grips with" means, to begin to accept or embrace a situation or problems. You can also use the expression "Come to terms with" in the same way. These phrases are usually used it the past tense but not always. Both terms are used in casual and formal contexts. Example: Manuel had come to grips with the fact that his team had lost. "Deal with" could mean, to attend to an issue or solve a problem. This would not be used in place of "come to grips". Example: She was left to deal with the mess. "Deal with" is not really a phrase unless you add "it"...."Deal with it" is usually a commanding sentence that one would speak to another person. It's a command to cope with a situation or problem. Because it is emphatic, it can sound rude. Example: My boss said, "I understand I did not give you enough time finish your project. Deal with it". (In a commanding sentence the pronoun "you" is implied.) Hopefully this helps. Cheers!

Kylee is right, although I would say it was wider than that. It can also be 'becoming experienced or familiar with'. e.g. "I'm only just coming to grips with the new safety laws". 'Deal with' has more of a 'finalise' aspect to it. In general you deal with a problem, but you might be able to come to grips with something without having to actually deal with any problems. Obviously you can 'deal with' people, in terms of making a deal. That's a different meaning. I assume you mean 'synonymous' rather than 'anonymous'?

It's similar. "Coming to grips with" is like have to face something or dealing with it.

I agree with Gary. "Deal with" is more genereal. You have to deal with work, deal with this paper due on monday, deal with this person, but "coming to grips" has less of a negative "chore" connotation to it. Example: I am "coming to grips" with this death, with a new idea, with your relality of the situation. In my opinon its more of an epiphany state of dealing with something. You werent aware of the entire scope of what you were dealing with, and now you are starting to.

Agreed. "Coming to grips with" something is active and takes effort; whereas, "dealing with" something is more final, like a one time event and often means giving up.