What are the differences between "Crawling peg" and "Crawl-like arrangement"?
The answer is already in your question. As the IMF paper says:

Classification as a crawling peg involves the confirmation of the country authorities’ de jure exchange rate arrangement.

So the difference between crawling peg and crawling-like is that in the first case country officially states that it is doing crawling peg, while with the crawling-like arrangement the country does not officially follow crawling peg, but behaves in a way as if it would be following it.