[Tree terminology]

[Christian G. Bower]

Brendan McKay <bdm at cs.anu.edu.au> wrote:
...
> 
> planar = ABLE TO BE drawn in the plane without crossings
> plane = ACTUALLY drawn in the plane without crossings
> 
> The difference between these two is critical when counting things
> since one object might be drawable in multiple distinct ways.

This distinction is important in graphs, but probably not in trees since
any tree can be drawn in the plane without crossings. Thus it is unlikely
an author would use "planar tree" with the definition you have given.
More like they mean "plane tree."