Pages are useful for long-form content, especially content that stays "static" over time (i.e., is relatively permanent and does receive frequent updates). Common uses of a page include an "About" section, a recipe, a product description, or directions to a location.
Like blog posts, news items are meant to show new information. They can be arranged to look just like blog posts, showing newest information first. News items are useful for giving service or event updates, reminding visitors about upcoming deadlines or projects, or releasing reports. Like a page, a news item is an incredibly flexible tool.