Spider is a program that scans web-page and collect data for indexing but crawler automatically follows links on webpage.
Spider is a browser like program that downloads web pages while Crawler is a program that automatically follows all of the links on each web page.
Spider: A browser that downloads website pages.
Crawler: A programme that follow web pages automatically.
Basically, there is no difference between spiders and crawlers. the working of both are same although names are different. Spiders and Crawlers are exactly same. It's the one that crawl your site for indexing and ranking. It can also be called as bots.
As far as i know both Spider and Crawler are interchangeably used and to some extent both are the same thing. But there are few people who define these two things separately like some calls Spider is a browser type program that helps to download web pages while Crawler is a program that automatically follows all of the links on each web pages.
In order to get deep insight you can visit en.wikipedia.org/wiki/Web_crawler
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