Of course, the two systems have diverged quite a bit; though kanji was brought into Japan several times throughout history, not just once.
At first, Japanese scholars used kanji to write in Chinese rather than Japanese. Eventually they moved on to using kanji to represent the sounds of the Japanese language phonetically rather than ideographically. It was during this time that you were likely to see kanji being used in words completely unrelated to their Chinese meanings (even today, some words are ateji and written with kanji based not on their meanings but their readings).
As time went by, kanji we're reworked into the familiar kana systems that we see today. This greatly simplified the writing system by allowing inflectional endings (okurigana) to be written in a semi-standardized way (since previously, any number of kanji could be used to represent the same phonetic syllable in Japanese).
So, that's one way in which they have diverged in the two languages. Yes, the Japanese have created some kanji, some kanji have evolved, and some kanji changed over the centuries in China to be reintroduced to Japan multiple times.
Also, Chinese went through a simplification process and many kanji (hanzi in Chinese I do believe) look radically different (sometimes only consisting of a small part of their original form) than they once did.
Yes, some kanji still retain similar meaning between the two languages, but nowhere near enough for a document written in one language to be intelligible to a speaker of the other.
An example of this divergence is 手紙. As far as I know, in both Chinese and Japanese, 手 means "hand" and 紙 means "paper". But while the compound meaning of 手紙 in Japanese is "letter", in Chinese it means "toilet paper".
