For the Byzantine tradition, 'Pentecost' refers to the Fifty Days (so that the 'Pentecostarion' is what modern Westerners might call a 'Paschaltide' book). This is in line with the Greek New Testament; compare "When the days of Pentecost were completed". It seems to me that the classical usage is to call Easter Sunday "the Pasch"; to call the Sundays following "Sundays after Pasch"; to give Pasch an Octave (during which the baptised wore their albae and were catechised) ending on Saturday, after which we say that we have finished (peregimus) the Paschal mysteries. Whitsunday is the day when the Fifty Days have been completed, and, if those Fifty Days are to have an official title, "Pentecost" is what they should be called.
In addition to this, we in the West have a concept of "Tempus Paschale"; "Eastertide", during which Alleluias are multiplied, Regina Caeli is said, and so on. The Easter precept can be fulfilled during this period. Traditionally it ends at None on the Saturday after Pentecost Sunday.
I surmise that misunderstanding has arisen from confusion between the "Days of Pentecost", i.e. the Fifty days which begin with the Pasch and last a week of weeks; and Tempus Paschale. I suspect that these two are not the same thing, despite the fact that treating them as such is at the basis of the Bugnini reform of the Calendar.
Everything above is really a question. I may have got it all wrong. I am seeking enlightenment and failing to find it in the standard places of refence.
Perhaps a reader can put me right!