An "auto-formatting" of an entity is an application of multiple formatting properties, or constituent item styles, on its contents. This is distinct from choosing a style. If we set the style of, say, a list - we do not consider that as having "auto-formatted" our list.

In this vein, and with us fleshing out the support for table styles as proper styles (see e.g. bug 152711 and bug 105933) - we should refer to Table Styles as what they are: Styles.

Thus:

1. On the menus, Table > "AutoFormat Styles..." becomes Table > "Styles..."
2. The "AutoFormat" dialog becomes "Table Styles" or "Table Style"
3. The Table Styles dialog "Format" heading label becomes "Styles" or "Current Table Style" or "Table Style" (the latter two emphasizing that the selection is the choice of style for the table for which we opened the dialog)
4. (possibly) The Table Styles dialog "New Style" button becomes "New". Only relevant if "Format" becomes "Styles" in item (2.).
5. (possibly) The Table Styles dialog "Edit Style" button becomes "Edit". Only relevant if "Format" becomes "Styles" in item (2.).
6. (possibly) The Table Styles dialog "Format" heading label may also need to change, not sure. Perhaps to "Properties" or "Style Properties" or "Properties to Apply"? 
7. The documentation should change in accordance with the above