In the book, Josh is explicitly upset about Lara Jean and Peter's relationship for a romantic reason, and his jealousy leads him to kiss her and admit he wants to be with her. The kiss has the double effect of making Lara Jean realise she is more into Peter than Josh and upsetting Margot when she learns that the two have kissed.
While the movie makes it clear that Josh doesn't like Lara Jean dating Peter, it's pretty vague about whether or not this is because of jealousy. It's easy to read Josh's actions as him just not approving because he thinks Peter will hurt Lara Jean. The kiss never happens in the movie, and Margot is upset at the revelation that Lara Jean has feelings for Josh.