Don't worry, I'm only just working this out as well
If a Phal grows a second growth from the base it is known as a Basil Keiki. The same is true of any Monopodial orchid. Monopodial orchids are meant to have only one growth point, but if that is damaged they may form another.
A Dendrobium on the other hand is a Sympodial orchid which means it naturally forms mutliple growth points from the base. Sympodial orchids generally stop growing annually and start new growth points shortly after.
The new growths on Sympodial orchids tend to just be known as just that... 'new growths'. But as a Dendrobium grows as 'Canes' the growths are also sometimes just called 'New Canes'.
Sympodial orchids can also form Keiki's but usually higher up on of the existing growths.