"Латвийка" and "латышка" are both translated into English as "a (female) Latvian" (or, which in English is a rather archaic form, "a [female] Lett"). But what is their difference in meaning? Is one of the forms archaic? Or does one mean Latvian by citizenship and the other means ethnic Latvian? Perhaps a person of Russian ethnicity who is from Latvia would prefer to call themselves by one rather than the other? I have consulted a number of dictionaries without getting any enlightenment.
Some nations have distinct words in Russian for "pertaining to the titular ethnic group" and "pertaining to the nation or state", as in "Russian" vs. "Russia's":
русский / российский
латышский / латвийский
казахский / казахстанский
малагасийский / мадагаскарский
This happens when the names of the country and the ethnic group come from the different roots (Germany particularly stands out in this regard across the languages of the world).
So латвийка would mean "a Latvian national or resident", while латышка would mean "ethnic Latvian".