For prayer, the appointed time acts as a surrounding interval: once a disapproved time passes, the same type of prayer may be offered during an allowable time. Starting a prayer at the disapproved time has its own rules, but later lawful performance is possible.
In a vowed fast on Eid, the specified day cannot be detached from that day’s act of fasting. The rules of beginning and continuing that fast therefore cannot be copied mechanically from those of prayer.
The relation of time to the act of worship matters when determining how performance can be made lawful or when it must be avoided.