Copy Options
There are two toggles to decide what a stamp actually copies from the Block Format into the target cells.
Apply content
Copies the template cell's value or formula. A blank template cell, one with no formula and no label, copies nothing, leaving the target's existing value alone regardless of whether Apply content is checked.
Apply style
Copies the template cell's styling: colors, number format, borders.
Column width and row height are not yet copied by a Block Format. See Limitations.
Overwrite and saving
When Apply content stamps a value onto a real, editable data cell (e.g. an Overwrite landing on an existing cell in a dataset, not a Row/Column space cell) then this value can be saved. It makes the Matrix widget dirty and Save persists the stamped value to the server, exactly as if a user had typed it in. This only happens when the stamped value's type matches the target cell's, e.g. a number stamped into a numeric cell.
The reverse is also true: a stamp has nothing to save when it lands anywhere else. Row/Column space cells have no data of their own to persist, and lines that a Block Formatting Rule inserts are never saved either, whatever they compute to: there's no original server value to compare against, so nothing is added to the change set. Only an Overwrite onto an existing data cell can make the Matrix saveable.