Linear model selection - Subset, Forward

We use 2**p model variations in order to define best model in subset selection. In contrary, we use 1 + p(p+1)/2 models in forward selection. But in the book it states,

"Since we perform guided search over model space, we utilize substantially more than 1 + p(p+1)/2 models in forward selection"

What does it imply?

Source — Introduction to Statistical Learning, Chapter 6.1.2, Page 209, footnotes.

Any recommendations appreciated.