"Custom Fields" are content elements that have been set up especially for your specific site. By using custom fields, we can make sure that certain pieces of content like text or images can be placed in the exact right spot with the exact right formatting.
"Page Templates" are pre-defined layouts and often include a pre-defined set of custom fields.
In the following example of a page template, the "Date" and "Banner Image" are custom fields:
You can see a page's template name by opening it up in the editor and looking at the "Page Attributes" box: