I see many similarities between Nazism and fascism, and some some sources say that Nazism is just a form of fascism. What are the differences...

Nazism certainly is a form of fascism.  However, Nazism
had aspects that are not necessarily part of fascism.  One
way to put it is to say that Nazism was a form of fascism that emphasized racism and
anti-Semitism.

Fascism is an ideology that emphasizes that
people's first loyalty must be to the state and the leader, not to the individual.  It
is an ideology under which all people must see themselves as essentially similar.  This
is where the term "fascism" comes from.  It comes from the idea of
"fasces," which were bundles of sticks tied together with an
axehead protruding from among them.  They symbolized how things that are weak on their
own (the sticks) can be very strong when united with others like them.  In a fascist
system, the individual people must band together unquestioningly and must make
themselves identical with one another.  In this similarity and commonality of purpose
comes power.

As you can see, this does not necessarily
assume racism.  People can feel that they are identical and can owe loyalty to a state
even if they are of different races.  The same goes for religion.  In Nazism, however,
the idea was that people could not be identical unless they were racially identical. 
This led to a very virulent form of racism and
anti-Semitism.

Nazism is a form of fascism because of its
emphasis on the idea that people should be identical and should be completely loyal to
the state.  However, it is different from other forms of fascism because it believes
that people of different races and religions cannot be identical enough to form the
metaphorical fasces.