Good question! Depends a lot on where in Europe. First, the Samaritans were more or less nonexistent in Europe, so all we can really look at are the Karaites.

The Karaites lived mostly in Eastern Europe, around Crimea, Ukraine, the Baltic countries and Poland. There used to be a karaite presence in Spain in the Middle Ages, as shown by the many „classical“ jewish polemics against Karaites that were written there between the 11th to 12th century. After their expulsion from Spain around the 12th century, they were mostly concentrated in the Byzantine Empire. To sum it up: we have to speak about Karaites only, and in Eastern Europe.

Looking at that: it changed over time. Depending on the circumstances, Karaites were sometimes treated as jews and sometimes differently. During the Chmielnicki massacres of 1648, Jews and Karaites were targeted, while the Jewish-Karaite relations at that time were especially good. Around 1700, christian scholars wrote a lot of books about the differences of Karaites and Rabbinic Jews and were certainly able to distinguish them, while we don’t know how the average person differentiated between them. When the area was taken over by Russia (end of the 18th century), both groups were treated very differently. As stated in the Encyclopaedia Judaica: „Until then, [their] external history [...] had been similar [...], both considered each other as Jews“. After Catherine II. passed a law in 1795 that did not require the Karaites to pay an extra tax imposed on the Jewish population, both groups were for the first time treated as different peoples by the government. In the years after that, Jewish-Karaite relations deteriorated rapidly. 1827, the Crimean Karaites were exempt from military service and by that were treated like the Crimean Tatars. By then, most or all of them spoke the Tatar language and were maybe sometimes even unable to communicate with Jews if they only spoke Yiddish.

In the end, it can’t be said for sure when regular people around them started to be able to distinguish Jews and Karaites. But we can see that around 1700, at least educated Christians were able to differentiate between them. Around 1800, Jews and Karaites started to be seen as completely different groups by others, used different languages in everyday life and, most importantly, didn’t consider each other Jews anymore. From here, we can assume that most people differentiated between the groups aswell.

TLDR: can’t be said for sure, around 1700, some people did, after 1800, most people probably saw them as distinct groups. By that time, they themselves did not consider each other Jews anymore. Sorry for possibly bad style, non native speaker and on mobile.

Edit: replaced misleading sentence and added some words.

Editedit: of course always happy to provide sources!