Core and layout overrides work in a similar manner, however have vastly different affects on your template and website. It is important to keep in mind that your template acts as the structure that contains the content and adds style to it. The content can dynamically change without affecting your template and vice versa. It's also important to note that extended template overrides are unique to the Construct framework.
Joomla core overrides are located in the
/html folder that is within your template directory and change the code produced by the core components and modules. They do not have any affect on the layout and style of your template. For example, if you'd like to change the single article table-based output produced by Joomla's core to use
<p> tags, you would do this with a core output override. You would copy
templates/je-construct-xxx/html/com_content/article/default.php and then edit that file to suit your needs. This core output override would only affect the markup produced by the core when viewing a single article layout and would not change template which contains it. To learn more about overriding Joomla's core output, read http://docs.joomla.org/How_to_override_the_output_from_the_Joomla!_core
Layout overrides change the structure and style of your template, without affecting the markup produced by the core. Extended layout overrides, which can be thought of as variations of your template's index.php file, are located in the root and subfolders of the
/layouts directory of your template. Extended style overrides, which dynamically add style sheets, are located in the subfolders of the
/css directory of your template.
As the template is the structure which positions the various pieces of content produced by the core (i.e. modules and components), the template can change without affecting the structure of the core content. For example, you may wish to change the width of
<div id="right"> on a particular category blog, and have it be another width on other pages. This would be done with an extended template override. While the appearance of the page changes by changing the template layout, the markup produced by the core does not change.