In the Catholic Church there exists a variety of liturgical rites, each with its own tradition.
One of the largest branches of the Church is the Byzantine family, which is in union with Rome. There does also exist the Eastern Orthodox Church, which is similar in many ways, but it is not currently in union with the Holy Father.
Each liturgical rite is able to pass on its own traditions and to determine which liturgical colors they wear on each feast.
While red was chosen for the Roman Rite on Pentecost, Byzantine Catholics continue their own tradition of using green for this feast of the Holy Spirit.
The Byzantine Catholic Archeparchy of Pittsburgh explains the symbolism on its website:
Since Pentecost was originally a feast of harvest, as was mentioned above, the Jews used to decorate their homes with the fruits of the harvest-flowers, green foliage, garlands etc.-in order to add more pomp and solemnity to their celebrations. This same custom was also adopted by the Christians. To them, however, the green branches and flowers took on a symbolical meaning-the divine life and gifts of the Holy Spirit.
Furthermore, “The green color of the foliage was accepted by our people as a symbol of divine life brought to us by the Holy Spirit. For this reason also, the clergy wear green vestments for the liturgical services on Pentecost and its postfestive period.”
Roman Catholics do recognize a similar spiritual connection with the color green during what is now called Ordinary Time.
Nicholas Gihr in his book The Holy Sacrifice of the Mass brings to mind the images of a tree and garden to explain its symbolism:
Green is in harmony with the very nature of the Church—she is a mighty tree, which lifts its top majestically toward heaven, spreads its shady branches and leaves in benediction over the earth, resplendent with the richest blossoms, bringing forth choice fruits of grace and virtue u in abundance. She is the watered garden of the Lord; Christ, the good shepherd, leads his sheep to ever green pastures. The Church clothes herself in green vestments to express her joyous, lively hope of the ever lovely and eternally verdant meadows of the heavenly paradise, of the incorruptible inheritance and the unfading crown of glory in Heaven.
Many Slavic countries celebrate Green Holydays after the feast of Pentecost, extending the celebrations of Pentecost for a full week.
And today we celebrate...