In modern, Western usage, they are the same game
Consider these two games:
1981 Pachisi by Whitman Games
1982 Parcheesi by Selchow & Righter (later republished by Milton Bradley)
Both of these have similar boards with only cosmetic differences. They also both use dice, are played individually rather than in teams, and have similar rules.
There are ...
Hopefully you are playing Pachisi and not Parcheesi. If yes, then this answer is accurate.
An ebook by Damian Walker here:
A Book of Historic Board Games
Page 25 - 1.2.7
A grace counts as if were a separate throw scoring 1, in addition to
the value of the cowries. Graces are used for entering and moving
As long as you have a grace at then ...