In the US we have only two parties, but many more 'interests'.
The Democratic Party traditionally served liberals, progressives,
labor, consumerism, etc. etc. The Republican Party served
conservatives, capitalists, libertarians, etc. Both parties at
different times served isolationists, racists, reactionaries,
expansionists, imperialists, etc.
When one of these interest groups feels its party doesn't serve
its needs, they will sometimes attempt to form their own parties.
The Progressive Party, the Free Soilers, the Know Nothings, the
'American Independent Party' (of George Wallace) are examples of
this.
In the case of the Progressive Party, Teddy Roosevelt was a very
progressive president in the Republican Party. In fact his time in
office was called 'The Progressive Era'. Roosevelt endorsed the
next American president, Taft, thinking Taft would carry on TR's
progressive agenda. When he didn't, Roosevelt got angry and decided
to run against him as a third party candidate. His party is called
the Bull Moose Party but that's a nickname, it was actually the
Progressive Party.
