TYPO3 Core

The description for both is pretty much the same.

The examples look very similar too. I honestly don't know what be.pageRenderer is for in comparison to be.container.

• be.pageRenderer

be.pageRenderer
ViewHelper which allows you to create extbase based modules in the style of TYPO3 default modules.

Examples
All options:

<f:be.pageRenderer pageTitle="foo" 
    includeCssFiles="{0: '{f:uri.resource(path:\'Css/Styles.css\')}'}" 
    includeJsFiles="{0: '{f:uri.resource(path:\'JavaScript/Library1.js\')}', 1: '{f:uri.resource(path:\'JavaScript/Library2.js\')}'}" 
    addJsInlineLabels="{0: 'label1', 1: 'label2'}" />
Custom CSS file EXT:your_extension/Resources/Public/Css/styles.css and JavaScript files EXT:your_extension/Resources/Public/JavaScript/Library1.js and EXT:your_extension/Resources/Public/JavaScript/Library2.js will be loaded, plus some inline labels for usage in JS code.

• be.container

be.container
ViewHelper which allows you to create extbase based modules in the style of TYPO3 default modules.

Examples
Simple:

<f:be.container>your module content</f:be.container>
“your module content” wrapped with proper head & body tags. Default backend CSS styles and JavaScript will be included.

All options:

<f:be.container pageTitle="foo" 
    includeCssFiles="{0: '{f:uri.resource(path:\'Css/Styles.css\')}'}" 
    includeJsFiles="{0: '{f:uri.resource(path:\'JavaScript/Library1.js\')}', 1: '{f:uri.resource(path:\'JavaScript/Library2.js\')}'}" 
    addJsInlineLabels="{0: 'label1', 1: 'label2'}" 
>
    your module content
</f:be.container>
“your module content” wrapped with proper head & body tags. Custom CSS file EXT:your_extension/Resources/Public/Css/styles.css and JavaScript files EXT:your_extension/Resources/Public/JavaScript/Library1.js and EXT:your_extension/Resources/Public/JavaScript/Library2.js will be loaded, plus some inline labels for usage in JS code.