Google’s John Mueller answered a question about whether it matters to indexing speed if Googlebot mobile or Googlebot desktop crawls a page. The person asking the question was worried about slow indexing and wanted to know if getting crawled by Googlebot desktop (instead of Googlebot mobile) was the reason.
Googlebot Desktop and Mobile
Google has a multitude of website crawlers that follow from link to link discovering new web pages to crawl and index.
