Term for animation style change that accentuates emotions/feelings
This is referred to as a "monologue" (モノローグ). It is essentially what is referred to as an externalzaton of character inner state and depending on the author, can include meta-action content between other characters. It's literally a figurative voice from a character's heart. The cut in anime is typically set up a a montage shot.

Monologue typically focus predominantly on one character at a time, in order not to confuse a reader or viewer. The depictions can vary drastically between series and genres. 

Chibi style monologue are intended to convey a lax atmosphere, cutting away from the norm or typical seriousness, a mood or tone shift as you will.





Alternatively, more detail can add seriousness or tension to the situation, application can vary depending on the skill and experience of the author and/or artist.