Dynamic and static
The dynamic text wrap allows you to move the wrap object around: it will dynamically re-wrap text on its position.
The cut-in creates a static hole in the text frames, so when you move the object, the hole remains.
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Scope differences
The dynamic text wrap affects frames and rules, i.e. it "engraves" itself dynamically only in underlying frames, while leaving intact boxes and images. On the figure left, the brown box engraved in frames, but image and yellow box were not affected.
The cut-in makes a static "hole" in boxes, rules and images too. Cut-in does not wrap text in tables. |
For more details on cut-in, see also: Use the cut-in (static wrap), Move or scale cut-in, Remove cut-in and Remove cut-in on large images.
For more details on dynamic wrap, see Toggle dynamic wrap, Wrapping text around images with captions and Limitations of dynamic wrap