Sections and Categories:

Sections and Categories in Joomla are used to organise or manage the articles. A section have one more categories and a category have one or more articles assigned to it. An Article in Joomla is associated with exactly one category. Sections concept is removed from Joomla 3.x. Now category plays the role of it. You can make one more categories and subcategories that are assigned to an Article. For example, Programming Language is a category and PHP, Java, C, C++ etc are sub categories. No you can put your articles inside these category or subcategory.

Articles/Content Items:

Articles/Content Items is a piece of information that you see in the web page of a site. It works as a container that contains text, images, links etc. Each article in joomla consist of exactly one category or subcategory. Articles can also be Uncategorised Articles. Uncategorised are those articles which are not associated with any articles.