Very few languages have a direct equivalent the English-language distinction between racism and bigotry. French does --- not surprising, considering that the English word 'bigot' is a borrowing from French in the first place. Dutch comes close with 'kwezel', although that's closer to the original French meaning of 'bigot' (an ostentatiously and superstitiously religious person).
But I've gotten in a number of discussions over the years with people who loudly (and wrongly) accused others (in Dutch, in Hebrew,...) of being 'racist' when plainly race was not even remotely the issue. (The closest you can come in Hebrew to the meaning of 'bigotry' is 'kanaut iveret', literally 'blind zealotry'.)
Narrowly speaking, "racism" refers to prejudices against other people based strictly on their biological/ethnic ancestry. The 19th Century proto-Nazi racial theorists such as Gobineau or Houston Stewart Chamberlain were plainly racist, as were essentially all who defended the 'peculiar institution' of slavery in the antebellum South or Jim Crow laws later.
By contrast, "bigotry" refers to prejudices against other people based on factors other than their biological ancestry, such as:
- their religious affiliation (or lack thereof)
- their country of citizenship or birth
- their region of birth within a common country
- their primary language
- their social class
- their gender and/or sexual orientation
- their political affiliation
- ...
For instance, many East Coasters and West Coasters harbor attitudes about people from the Deep South that are condescending at best and bigoted at worst --- but such attitudes are not based on race but generally on the (real or perceived) deep religiosity and conservatism of Southerners. The enmity between Flemings and Walloons --- based not on any significant differences in ethnicity or general culture but principally on their different languages --- is another example of bigotry that is not racist.
The sort of religious person who believes everybody not of their particular faith to be some sort of hell-bent heathen is plainly a bigot. But so, in their own way, are anti-religious fanatics like Richard Dawkins (or his Belgian wannabe Etienne Vermeersch). Neither type is (necessarily) a racist.
Many people on the political "left" hold startlingly bigoted prejudices about people (mis)identified with the "right" --- and conversely. Usually, these prejudices have little if anything to do with race.
Of course, names for some forms of bigotry have become rhetorical clubs to beat one's opponent to death with. I remember, for instance, when "homophobia" was a clinical term for an actual psychiatric condition --- an obsession with, and fear of, homosexuals fueled by deeply repressed doubts about one's own sexual orientation. Nowadays, anybody who has any misgivings at all about certain attempts to canonize the homosexual lifestyle --- for instance, those who feel tolerance or acceptance should be enough, or have second thoughts about children being raised by two men --- risks being labeled a "homophobe". Or, for that matter, anybody who is less than enamored with certain dysfunctional aspects of black urban culture in the US --- which, as Thomas Sowell persuasively argues, is actually not so much authentically black as an adaptation of the self-destructive "redneck culture" of their erstwhile white oppressors --- or simply cannot stand rap "music", risks being labeled an anti-black racist --- often by people who would not think twice about using crude anti-black stereotypes against blacks that they disagree with politically. On any opponent of unrestricted immigration to the USA or of blanket amnesty and services to illegal immigrants risks being labeled an anti-Latino racist --- disregarding the fact that many legal first-generation immigrants themselves are at best ambivalent about those whom they perceive as 'gate-crashers'.
In a similar way, apologists for radical Islamism and Islamic terror attempt to brand any form of criticism of same as "Islamophobia" --- even criticism on the part of people who, like Daniel Pipes, are at pains to make a distinction between Islam and radical Islamism.
A more jocular/tongue-in-cheek use of the term "bigot" exists, generally referring to 'bigotry' based on such seemingly innocuous factors as one's preferred sports team or computing platform. Every so often, posters on Macintosh (or Linux) forums will accuse obtuse webmasters or IT managers of "anti-Mac bigotry" or "Windows bigotry". (In many cases, webmasters refusing to make their side cross-platform are simply too incompetent and/or lazy to code to standard --- I know plenty such clowns here who loudly rationalize their own sloth by claims about the "marginality" of Macs or Linuxen.)
The related term "zealotry" is generally reserved for people whose greatest hatred is reserved not so much for adherents of a different religion/ideology/... but for their less fanatical fellow travelers. Sweeping in front of my own doorstep, I know quite a few pro-Israel zealots who will consider anybody advocating a course less radical and/or fanatic than their own to be "court Jews", "kapos", "Jewish antisemites" and the like --- and yes, even proud lifelong Zionists like this writer find themselves on the receiving end of such abuse sometimes. Ironically, the most fanatic zealots are often those who choose not to come share our fate --- and I have as little time for such "armchair super-Zionists" as I have for the type of anti-Israel bigot that would impose suicidal moral standards on Israel without having to suffer the consequences of their own sanctimoniousness.
Is antisemitism racist or bigoted? Personally I prefer the term "judeophobia" over the done-to-death "antisemitism", but the answer is: depends. Antisemitism can be a form of racism if it is primarily rooted in hatred for allegedly inferior/degenerate ancestry --- such as Nazi antisemitism. One still does find this type of anti-Jewish racism in some circles (neo-Nazi as well as Arab), but far more common nowadays is antisemitism as a form of bigotry. Anti-Jewish bigots (particularly those on the "left") are often at pains to deny that they hate Jews for being born Jewish ---
they "merely" hate people who 'behave Jewish', who practice the Jewish religion or are otherwise unwilling to assimilate into the majority faith, or who identify with the 'racist'/'oppressor'/... State of Israel... In many instances, the protestations of non-racism may well be sincere at least on the conscious level. Thus one sometimes sees the bizarre spectacle of prominent and outspoken judeophobic bigots ostentatiously participating in Shoah memorial ceremonies or producing art/movies/... commemorating the Shoah.
(As an aside, let me comment on the distinction between cant and hypocrisy. The hypocrite is generally quite well aware of the dissonance between his/her words and deeds, while the peddler of cant is generally him/herself unaware of the chasm.)
Finally, of course, no discussion of bigotry would ever be complete without quoting G. K. Chesterton:
It is not bigotry to be certain we are right; but it is bigotry to be unable to imagine how we might possibly have gone wrong.