Both mean ”pertaining to Finland”, but finsk is often used as ”pertaining to the Finnish-speaking population of Finland” contrasting with finlandssvensk, which refers to the Swedish-speaking. Finländsk is the neutral term and is just ”pertaining to Finland” in general.
Finns are often clearer with this distinction whereas Sweden-Swedes colloquially use finsk and finländsk quite interchangeably. But Swedish-speaking Finns (as I’ve heard) would find it plain incorrect if someone wrote that ”Tove Jansson var en finsk författare” instead of finländsk or finlandssvensk, since she wrote in Swedish and not Finnish.
The hover feature showed that "en... till" means "to another," but my translation (They are going to another Finnish city) was not accepted. I am deducing that "en... till" as to be in that exact order to mean "another." In that case, my sentence should actually be "De åker en till finländsk stad?"
I'm afraid that's a bug, I'll look into it. en … till means another like in one more, but of course it should not be shown here, it doesn't even say en … till but till … en.
If you want to say They are going to one more Finnish city, that would be De åker till en finsk/finländsk stad till.
Since "mot" and "till" both indicate that they are going to or toward that direction, that would not make sense. You need to use "från" to show where they come from.
Also, be careful here, since both Helsinki and Moscow have other names in Swedish.
A correct sentence would hence be:
De åker från Helsingfors till/mot Moskva
De åker till/mot Helsingfors från Moskva
There is some different ways to do that, and it depends a bit on the circumstances. But one way is: Åk mot Moskva tills du kommer till Helsingfors. (Go towards Moscow, until you come to Helsinki).
Since an imstruction like this are likely used when driving by signs that don't (to begin with) have the city you are going to, it is common to say "Följ skyltarna mot Moskva. När du kommer till Helsingfors ...." (Follow the signs toward Moscow. When you come to H...)