Actually I believe only one was an algorithm update, where the other, Penguin, was a specifically targeted bit of software aimed at devaluing sites with lots of unnatural, spammy links pointing to them, which is why it's got webmasters panicking like headless chickens and constantly trying to email all the low quality directories they submitted their sites to over the years to get their links removed, or contacting the thousands of blogs they had comment spammed, often via cheap SEO's on digital point, to have their comments removed.
so in big words we can say, panda check your on site seo things and penguin check for your offsite external backlink quality.
Google panda decreases ranking for sites containing large amount of advertisement and having a low quality content. it mostly focus on Quality. Where as Penguin update drop in ranking for sites which use unethical Black hat techniques that break SEO rules.
Panda and Penguin both are google's updated algorithm, regarding low quality and spammy activities (against google webmaster guide line) Panda focused on low quality content and copy from any where others, where as penguin strictly focus on low quality links with over optimization.
Panda - To stop over optimization by means of stopping low quality links, over optimized anchor text and keyword stuffing. However, it loves natural backlinking. Penguin - More of a quality ensurer for google. This check content quality to avoid content farms, thin content and high bounce rates.
Simple Definitions Google Panda:- All about fresh and quality content Penguin:- All about quality links. But in Google Panda few sites were hit by Panda those had low quality or copied content and few sites got high ranking those had good quality and informative content. But in Google Penguin:- The websites got panelized and few were banned from Google search results.