Check out the PHB
The PHB approaches the game more from the player side while the DMG approaches it from the GM's side. This means, generally speaking, roleplaying descriptions in the DMG are focused on NPCs and how GMs can roleplay them effectively, while roleplaying descriptions in the PHB are more focused on how players can effectively play their characters. The second quote from the DMG provided in the question is from a section to help GMs recognize what kinds of players are playing. If you read the entire section on page 6 of the DMG it is more describing a player type than a method of roleplaying or acting.
There are some suggestions in the DMG for rewarding players for inspired role playing, for example the Inspiration rules starting on DMG 240. I find Inspiration points to be fun and helpful with both beginners and advanced players.
Descriptive and Active Roleplaying
For a good description of Descriptive Roleplaying and Active Roleplaying, which may be what you are looking for, check out PHB 185. Under the heading Roleplaying the PHB states:
There are two styles you can use when roleplaying your character: the descriptive approach and the active approach. Most players use a combination of the two
Later on PHB 186 under the Descriptive Approach to Roleplaying header the PHB offers this summary (after a more detailed description):
When using descriptive roleplaying, keep the following things in mind:
- Describe your character’s emotions and attitude.
- Focus on your character’s intent and how others might perceive it.
- Provide as much embellishment as you feel comfortable with.
Don’t worry about getting things exactly right. Just focus on thinking about what your character would do and describing what you see in your mind.
This sounds similar to the first quote in the question and may be what you were thinking of.
Active roleplaying is more like acting and shows the other players and GM what your character is doing rather than telling them what your character is doing. PHB 186:
When you use active roleplaying, you speak with your character’s voice, like an actor taking on a role. You might even echo your character’s movements and body language. This approach is more immersive than descriptive roleplaying, though you still need to describe things that can’t be reasonably acted out.