More than semantics
As Gordon Smyth mentions in the comments, it is more than just semantics. Due to the parameter $\phi_1$ the logistic growth model is not exactly equal to the logistic function used in logistic regression.
Compare
$$\phi_1/\lbrace 1+\text{exp}[-(t-\phi_2)/\phi_3]\rbrace$$
with
$$1/\lbrace 1+\text{exp}[-(t-\phi_2)/\phi_3]\rbrace$$
Logistic regression and fractions
Logistic regression deals with $\phi_1=1$. This relates to fractions between zero and one. The example from the book is a growth model and a different setting.
Not all fractions are logistic regression
Sidenote: I am saying that logistic regression relates to fractions, but not all fractions relate to logistic regression.
When we deal with fractions then we still might have $\phi_1 \neq 1$ for instance the fraction of coronavirus variants relates to growth models, and has been modeled by some with logistic curves that wrongly assume $\phi_1 = 1$.