Actually, I'm inclined to agree with you, Carlos, that Robert Cornysh and William Cornysh (II) are the same, and I've added Robert as an alias for this William.
On to elder versus younger. The tide has recently been turning, Grove notwithstanding. It is now becoming more and more widely accepted by music scholars that William Cornysh (II) - the elder (ca, 1430? - 1502) - was the composer of Gaude virgo, mater Christi, Salve regina, and possibly Ave Maria, mater Dei from the Eton Choirbook, as well as Magnificat from the Caius Choirbook. Notably, in the most reissue of "The Sixteen:The Crown of Thorns (Eton Choirbook series, Vol. 2)", the Stabat Mater is listed as being by "Cornysh (I), William", while on "The Sixteen:An Eternal Harmony" the Ave Maria, mater Dei is listed as being by "Cornysh (II), William" but the Salve Regina by "Cornysh (I), William". The Cardinal's Musick "William Cornysh:Latin Church Music" recording asserts all four of the above works are by William Cornysh the elder:
This disc contains all the music left to us in a complete state by William Cornysh the elder, and in so doing draws attention to the difference between the two composers named William Cornysh – the father and the son. The father is the composer of the Latin church music in the sweeping pre-Reformation style: the son, the writer of pieces in English and courtly songs. David Skinner’s research, printed in the CD booklet, provides the evidence and makes the connection between the Cornysh Magnificat and two other setting of the same text by Edmund Turges and Henry Prentes which obviously use Cornysh’s work as their model.
Elsewhere, from Answers.com we have:
The Eton Choirbook, compiled for liturgical use at Eton College around 1500, provides a unique view of English music at the turn of the sixteenth century; no other comparable repertoire source for this time has survived the depredations of the English Reformation. Among the 25 choice composers represented stands the name of William Cornysh, contributing eight pieces to this national anthology of devotional music. He also composed 13 of the secular part songs in a 1520 anthology of music known as Henry VIII's Songbook, after its collector and principal contributor. Clearly Cornysh held the respect of King and Church alike; very little straightforward information about his life, however, survives. In fact, recent scholarship suggests that these two repertoires may be the work of two separate individuals: William Cornysh the elder, composer of the mature Eton Choirbook church music, and William Cornysh the younger (possibly his son), actor, singer, and courtier.
And from Wikipedia:
The traditional ascription of all the works to Cornysh junior is the one more generally accepted. However, the possibility that the Eton works are the works of a generation earlier remains, and has interesting implications if true.
Finally, there is a complete page in HOASM about William Cornysh 'senior' setting forth the argument that the provenance of the Eton and Gaius Choirbook works are by the elder Cornysh.
Since these represent recent (as opposed to traditional) scholarship, I'm inclined to agree with this new view - at least for now.