The film — written by Kubrick and Clarke — came first. The book is a novelization of the movie. So watch the movie. It’s unlikely you will be disappointed.
They were written at the same time, but the movie was, indeed, released first. Completely agree that the movie is worth watching. I read the book first, which I felt made the movie more enjoyable for me, since it made the ending a lot more understandable.
No, the post you're responding to is mistaken. They were both written at the same time. It sounds like Clarke and Kubrick got together to hash out the plot and some of the details, then went off and each made their own version. The film was released first (barely, and apparently to the annoyance of Clarke), but the novel was not based on it at all.
“The screenplay was written by Kubrick and science fiction author Arthur C. Clarke, and was inspired by Clarke's 1951 short story "The Sentinel" and other short stories by Clarke. Clarke also published a novelisation of the film, in part written concurrently with the screenplay, after the film's release.”
Clarke himself provides additional details of the process, as well as omitted excerpts and scenes, in The Lost Worlds of 2001 (1972):
<https://en.wikipedia.org/wiki/The_Lost_Worlds_of_2001>
<https://archive.org/details/lostworldsof20010000arth>