On-page SEO is the practice of optimizing individual web pages for higher ranks on search engines. It includes optimizing content as well as the HTML source code of a page.
Off-page SEO on the other hand refers to the optimization of factors that fall outside the website spectrum like links and external signals.
While you have complete control over the elements that come under on-page SEO, when it comes to off-page SEO, you cannot gain absolute control over its components. For instance, if you replace low-quality images on the web page with higher quality, that is optimization through on-page SEO. On the other hand, if you share links to your website personally, it is off-page SEO.