There is written Cantonese that is slightly different from written Mandarin, but the vocabulary is similar enough that it is mutually intelligible. It's about as different as American English and Indian English.

Most of the time when writing Cantonese, you will write it in "formal" terms which are technically pronounced differently. So instead of a casual word, you will write the formal equivalent, but when reading it back you can transcribe it on the fly to the informal equivalent again. If you know Cantonese, you can watch TVB news reports with the subtitles on and you'll see this being done when they interview people.

For example, the word "without" in Cantonese is 冇 (mou), and in Mandarin it is 没. But a Cantonese speaker will still write "mou" as 没, or 無, even though those characters are supposed to be pronounced "mut" and "wu" in Cantonese and are considered formal. When reading it back, you can either say "mou" or "mut"/"wu" and both are considered fine, it just depends on how formal you want to be.

Another thing is that Mandarin is written exactly as it is said, and if you then read the writing back in Cantonese, it is completely intelligible, it just sounds overly formal and terse. So a Mandarin speaker can write something down and a Cantonese speaker will understand it. A Cantonese speaker can write something down using very formal terms and the Mandarin speaker will also be able to read it.

You can write Cantonese using the actual characters for the informal terms but then only Cantonese people will be able to read it since the characters used aren't commonly used in Mandarin. Even then many Cantonese speakers only know how to read/write the formal version and will have to guess at the "informal" version.

Another interesting thing is that there is actually a lot of shared vocabulary between Cantonese and Mandarin. In fact, most of the "formal" vocabulary is shared and exactly the same, since the both derive from Classical Chinese. Classical Chinese is really just "peak formality" of regular Chinese (all dialects). Thus if you write in Classical Chinese most educated Chinese speakers will be able to read it! This is why Chinese is described as "the oldest language in the world". An example is a no-smoking sign. In informal Cantonese, it's 唔好食烟, which is nonsense to a Mandarin speaker. It would literally mean "?? good eat smoke" in Mandarin (the first character is almost never seen in Mandarin). But you can write the formal term, which is 禁止吸烟, which is exactly the same and 100% readable in both Cantonese and Mandarin. It means "smoking is prohibited" in both languages.

I kind of lost track of my sentence there and double referenced the fact that I was talking about written language. There's a theory that it was to keep the people from being able to read older Chinese manuscripts and books which might make people question the communist party. Taiwan as far as I'm aware didn't adopt Simplified Chinese and the literacy rate is high, so at least the goals of the CCP (literacy) were achieved through better education instead of changing the language.