In the illustration below, the association between variables $x$ and $y$
is positive. (Variable $y$ tends to increase as variable $x$ increases.
Also, the relationship between variables $x$ and $y$ is
strictly monotonic (every increase in $x$ is accompanied by an increase in $y.)$
Thus, Spearman correlation is $1.$
However, the relationship is not linear (as you can see from the plot below).
Thus, Pearson correlation is smaller than $1.$
Computations in R:
x = 1:20
y = x^4
cor(x,y) # Pearson correlation
cor(x,y, meth="s") # Spearman correlation
Now, we add a small amount randomness to
y and call the result
The randomness destroys the strictly monotone relationship between
z. While the
xs are still in increasing order, the first two values of
z are out of order.
The change is too small to see on a plot, but the Spearman
correlation is no longer exactly $1.$
z = y + rnorm(20, 0, 10)
 10.001420 4.266542 72.025146
cor(x, z, meth="s")