It is not really a question of inner forms. What happens is that the
<em>algebraic group</em> $G_2$ has an extra endomorphism $\varphi$ whose square
is the Frobenius map (over the appropriate finite field). Just as for any
algebraic group over a finite field $F$ its rational points over $F$ are the
fixed points of the Frobenius endomorphism the Suziki groups are, by definition,
the fixed points of $\varphi$. Again, just as the Frobenius, on points over the
algebraic closure of $F$ $\varphi$ is an automorphism of the abstract group.
However, that is misleading, the essential points is that it is an endomorphism
(which definitely is not an automorphism) of the algebraic group. Most of the
properties of points over $F$ of a semi-simple algebraic group $G$ defined over
$F$ follows from the algebro-geometric theory of $G$ and the properties of the
Frobenius endomorphism. Similarly, most of the properties of Suziki groups
follows from the algebro-geometric theory of $G_2$ together with the properties
of $\varphi$. As $\varphi$ is very similar to the Frobenius endomorphism this
works almost the same way as if $\varphi$ were indeed a Frobenius endomorphism.