Is it true in the sense relevant to climate change?

Climate change is a lot of different things. For the statement that the count matters and a "tree is a tree",

Carbon sequestration? A giant redwood stores more carbon than a fir.

Healthy ecosystems? Different trees fit into different roles in a healthy forest.

The loss of biodiversity? Once a forest dies, a new forest somewhere else doesn't bring back the lost biodiversity.

In theory, Carbon sequestration is the closest to "a tree is a tree", you can plant large amounts of fast growing trees can capture more carbon over time, but that's specifying the later tree, which then matters.

No, a 3 foot tall sapling and a 300+ foot tall monster are both one tree but have very different impacts on the climate.

Fast growth commercial forests have high density because the individual trees are relatively small with a vastly smaller amount of root mass.

If I remember correctly, the youngest trees convert the most co2 (makes sense, they grow the fastest).