During the Umbraco request execution, an MVC Action is called which executes a Razor view to render content to the end-user,
Whenever a content item is rendered on the front-end, it is based on a model of type IPublishedContent. This model contains all of the information about the content item associated with the current request.
If you are working in a custom MVC Controller's action, a model of type ContentModel will be provided in the Action's method parameters. This model contains an instance of IPublishedContent which you can use.
When you are working in a View of type UmbracoViewPage (which is the default view type), the Model provided to that view will be IPublishedContent. For example, to render the current content model's name you could do:
All Umbraco view page types inherit from UmbracoViewPage<TModel>. A neat trick is that if you want your view Model to be IPublishedContent you can change your view type to UmbracoViewPage and the view will still render without issue even though the controller is passing it a model of type ContentModel.
IPublishedContent is a strongly typed model used for all published content, media, and members. It is used to render content in your views for your website.
UmbracoHelper is the unified way to work with published content/media on your website. Whether you are using MVC or WebForms you will be able to use UmbracoHelper to query/traverse Umbraco published data.
IMemberManager is an user manager interface for accessing member data in the form of IPublishedContent. IMemberManager has a variety of methods that are useful in views, controllers, and webforms classes.