You agree to do something or you agree to the demands of the company means you accept right, but you're generally agreeing with to do something, agree with means, share an opinion or agree with the rules, agree with someone means you share an understanding that you accept the same thing, so very similar, agree about again.
你同意做某件事,或者你同意公司的要求,意味著你接受了權利,但你一般是同意做某件事,同意的意思是,分享意見或同意規則,同意某人的意思是你分享一個理解,你接受同樣的事情,所以非常相似,同意再次。