Tridion DXA (Traditional/Decoupled)

I am oversimplifying... but here's what applies to Tridion.

• Basic Tridion (since 1999) is a decoupled CMS (Content Management and Website/Delivery are separate applications that can run completely isolated from each other)
• Headless CMS is one where the Delivery of content for a website is done over webservices and there is no "CMS logic" inside your application. This allows for "easy" building of applications that consume content from your CMS from any platform (mobile apps, your own platforms, etc)
• Tridion has been headless since 2015, when "Web 8" was released.

An application using DXA uses a headless framework to talk to Tridion's Content Delivery services.

In this scenario, Tridion remains a decoupled CMS, with Headless Content Delivery.

To cover the remaining 2 scenarios, which do not apply to Tridion:

A Traditional CMS is one where both Content Management and Website/Content Delivery run from the same application. This usually has the benefit of perceived performance - there is no "publishing", just a flag setting the content as "live" - but has the side effect of potentially exposing content that is not approved/live to your audience.

To be honest, I have no idea what is a progressively decoupled CMS, sounds like a made-up-marketing-word to say "we want to be decoupled but we're not there yet".

Hope the above makes sense.

EDIT

I just saw you tagged your question with 2013-SP1. Tridion 2013 SP1 is not headless, it is decoupled. Headless was introduced in the following version of Tridion. Also, as the name implies, Tridion 2013 is 7 years old and as far as I know is out of support (or will be soon).