Ultra rare species are unique animals that can only be purchased with real money or Wildlife points. Because of this, ultra rares cannot be purchased for a player and transferred to another zoo through gifting (unless they are Limited Editions or from the Limited Edition gifting tree).
If something were to happen during the gifting process, we would not want our players to be out real money or Wildlife points they purchased with real money.
There is an option to buy ultra rares for Zoomates but this only applies to promotional ultra rares through Limited Edition animals and gifting tree campaigns.
Ultra rare animals are excluded from the achievement levels that require a certain number of every species you own. They will generally have 4 stars and animate on your islands!