Ethnic parties aim to represent an ethnic group in a political system, be it a sovereign state or a subnational entity. An alternate designation is 'Political parties of minorities', but they shouldn't be mistaken with regionalist or separatist parties, whose purpose is territorial autonomy.
Historical ethnic parties
The oldest prototypes of ethnic parties are the Jewish parties of the Russian and Austro-Hungarian empires, e.g. Bund, Folkspartei, Agudat Israel, and the Swedish party in Finland, Svenska Folkpartiet (SFP), all of them founded in the end of the XIXth century or in the first decenniae of the XXth.
Ethnic parties and political ideologies
Ideological options may be totally opposite among ethnic parties.
For instance, between the parties competing for Jewish votes in interwar Poland and Lithuania, i.e. Zionist parties (themselves divided into Revisionist, General or Labourist parties), Agudat Israel (Orthodox religious party), Bund (marxist) and Folkspartei (interclass).
In some political systems, party politics are exclusively based on ethnicity, as in Bosnia-Herzegovina and its federal regions, in Israel, in Surinam, in Sabah, in Sarawak or in Guyana. The most extreme case is Fiji, where there are separate electoral colleges for each ethnic group, as there was in the pre-Israel Palestine Jewish Assembly, the asefat ha-nivharim, with separate 'curiae' for Ashkenaz, Sepharad and Oriental, and Yemeni Jews, or in present-day New Zealand for the Maoris (Maori Option).
As a consequence, it would be somewhat irrelevant to classify some parties in these systems as 'ideological' (social-democrat, liberal, christian-democrat etc.) and some others as 'purely autonomist', 'purely ethnic' or 'purely minority' parties.
The SFP is a full-fledged member of the Liberal International, as well as the Movement for Rights and Freedoms, representing the Turkish minority in Bulgaria, the South Tyrol People's Party SVP (grouping German- and Ladin-speaking inhabitants of Italian Alto Adige province) is a member of the Christian Democratic European People's Party, whereas the SDLP, an Irish Catholic party in Ulster/Northern Ireland is a member of the Socialist International, etc..
In interwar Poland, Jewish, German and Ukrainian parties never attracted all Polish Jews, Germans and Ukrainians of whom some were members of 'national' ideological Polish parties, mostly the Socialist and Communist parties, more open-minded than some conservative or 'progressive' nationalist parties who sometimes expressed violently antisemitic positions.
Ethnic parties and electoral systems
Common lists or electoral agreements can be organized either between ethnic parties (Flemish 'Kartel' for municipal elections in Brussels, the coalition for the 2001 parliamentary elections in Bulgaria between the - mostly Turkish - Movement for Rights and Freedoms and the Roma party Euroroma) or between two parties having common ideological options beyond ethnic differences, as the Bund and the 'Polish' socialist party PPS for the municipal elections in 1939.
Some ethnic parties are only taking part into substatal electoral competition, thus making them somewhat invisible to outside observers: the SSW in Schleswig-Holstein, the German parties in Denmark and Poland, the Roma parties in Slovakia.
It can occur that a single 'supra-ideological' party achieves, with varying shades of success, the representation of a whole ethnic group, as for the Svenska Folkpartiet in Finland, the South Schleswig Voter Federation for Danes and Frisians in the German Land of Schleswig-Holstein, the Unity for Human Rights Party for Greeks in Albania, the Slovenska Skupnost for Slovenes in Northeastern Italy, the Movement for Rights and Freedoms for Turks in Bulgaria, the Democratic Union of Hungarians in Romania.
In most cases, ethnic parties compete inside electoral systems where voters aren't compelled to vote according to ethnic affiliations and may vote too for 'non ethnic', 'transethnic' or 'supraethnic' ideological parties. In most Near Eastern Arab countries, the only such parties were the Communist parties, whose founding fathers and subsequent leaders came mostly from the Jewish, Armenian, Kurdish or Shi'ia minorities. The socialist movement in Thessaloniki (present Northern Greece) during the last decenniae of the Ottoman Empire was divided across ethnic lines between the Sephardi Jews (who formed the majority of the population), the Bulgarian and Macedonian Slavs and the Greeks, but all groups united when it came to FPTP elections.
'Intraethnic parties', or political parties inside diasporic communities
There is also a specifically diasporic type of political parties that could be labelled as 'intraethnic parties', i.e. parties that compete only inside the ethnic group political sphere.
The Jewish and Armenian (Dashnak, Ramgavar, or Hentchak) parties belong to this category, as well as the abroad sections of national parties, such as the (U.S.) Republicans Abroad and Democrats Abroad, the (British) Labour Party International, the (French) Parti Socialiste's Fédération des Français de l'Etranger or the American and European branches of the Israeli Likud and of the Kuomintang (Nationalist Party of China).
There can also be specifically diasporic political groupings, such as the Association Démocratique des Français de l'Etranger (left-wing) and the Union des Français de l'Etranger (right-wing), both competing for seats in the Conseil Supérieur des Français de l'Etranger, or the various political lists competing for the Comitati degli Italiani all'Estero (COMITES).