Nazism, yes.
But that’s not necessarily the case with fascism.
As already correctly noted, fascism exists as a sub-spectrum on the right side of the political spectrum, where there is considerable variation on that sub-spectrum.
Actual fascism can exist absent wars, death camps, and anti-Semitism.
Fascism as it exists today and as practiced by conservatives and rightwing politicians is anti-democratic and fundamentally illiberal*; authoritarian and seeking to compel conformity and punish dissent, the fascist right advocates for more power to the state at the expense of individual liberty.
Opposition to immigration and immigrants, fear of diversity, dissent, and expressions of individual liberty, and the propensity for one-party minority rule are all basic components of the fascist right.
It is therefore perfectly appropriate and warranted to be concerned about the rise of, and support for, fascism – democracy is indeed under attach by the fascist right.
*illiberal
opposed to liberal principles; restricting freedom of thought or behavior.
synonyms: intolerant · narrow-minded · unenlightened · puritanical · fundamentalist