A Mac notebook can be set to display two different ways when attached to an external screen. One way is to mirror the two displays. This means both will use the exact same format and show the exact same information. The highest common format the two screens support will be the default. Since one is 16:9 and one is 16:10, there will be black bars surrounding the image on one screen or the other.
The other way a Mac can run the second screen is independently, called extended desktop mode. Under that scenario (mirroring turned off), the two screens are free to display whatever is their native format, so the 16:9 will display a 16:9 format and the Mac will be at its native 16:10.
As to what will be the available resolutions for the 16:9 external display, that is established by the display's EDID, not the Mac, so the question can't be answered. There are really few limits on the Mac in this regard. Depending on the display, the Mac should be able to output formats like 1920 x 1080, 1280 x 720, 2048 x 1152, 1600 x 900 just to name a few.