Lightbox vs Dialog layer vs Layer Layer

You're right that a Dialog layer is a lot like a Lightbox slide. You need triggers to open and close it. When it's open, the user can't interact with the rest of the Player. 

Differences:

• A Lightbox puts a reduced-size version of the lightboxed slide over the center of the entire Player area. A Dialog layer is full-size content that stays within the slide dimensions.
• You have some options to customize how a Dialog layer covers the rest of the Player. (https://articulate.com/support/article/Storyline-360-Dialog-Layers#background-color ). You can't customize how a Lightbox covers the rest of the Player.

The Dialog (modal) option was added to layers to improve accessibility. When a Dialog layer is open, the program only focuses on the objects in that layer. (The article connected to the first link in your post has more info about this.) 

Which to use when? Short answer: It depends.

Here are some considerations/suggestions:

• Use a layer for content directly related to a given slide. 
• Use a Lightbox for content that applies across multiple slides when the user doesn't need to see the content on the slide below it. For example, I sometimes lightbox a custom Resources slide and provide access via a Player tab. (Here's more about that: TIP: Create Custom Player Tabs for Your Resources, Glossary, and More - Articulate Storyline Discussions - E-Learning Heroes)
• Use a layer on the Master Slide for content that applies across multiple slides when the content needs to appear in a specific position within the slide dimensions. (Here's more about that: Multi-layered dialog slide navigation - Articulate Storyline Discussions - E-Learning Heroes)