Investigation: I checked out "%APPDATA%\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar" and found links to "Nightly" and "Nightly (2)" which both open Nightly.
Bug 1495295 Comment 13 Edit History
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Investigation: I checked out "%APPDATA%\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar" and found links to "Nightly" and "Nightly (2)" which both open Nightly. I deleted "Nightly (2)" then opened and pinned Nightly. As I expected, it became "Nightly (2)" and created the link with the same name in the TaskBar folder. So, I deleted both links, reopened Nightly, and pinned it. The pinned icon and its link in TaskBar are now called "Firefox Nightly" and work properly while pinned. However, if I unpin it, the same issue with the context menu being incomplete appears.
Investigation: I checked out "%APPDATA%\Microsoft\Internet Explorer\Quick Launch\User Pinned\TaskBar" and found links to "Nightly" and "Nightly (2)" which both open Nightly. I deleted "Nightly (2)" then opened and pinned Nightly. As I expected, it became "Nightly (2)" and created the link with the same name in the TaskBar folder. So, I deleted both links, reopened Nightly, and pinned it. The pinned icon and its link in TaskBar are now called "Firefox Nightly" and work properly while pinned. However, if I unpin it, the same issue with the context menu being incomplete appears. Pinning Nightly to the taskbar from Start creates a new icon called "Nightly" on the tooltip and context menu. The context menu has only two options: "Nightly" and "Unpin from taskbar".