I know about buses and ferries, Rail transport in Finland page does not say if they are passenger trains
VR page shows only trains to Russia.
No, there are no passenger trains between Finland and Sweden. There is actually a train line crossing the border between Haparanda and Tornio, but it is currently (since 1988) only used by freight trains.
Coming from Sweden, you could take a train to Luleå, from which you have to bridge about 160km on the bus to Kemi, where you will have access to the Finnish passenger train network again.
According to EGTRE, the single rail border crossing between Sweden and Finland carries freight only.
Sweden and Finland use different track gauges, and freight is transshipped between Swedish and Finnish cars in Haparanda. The line across the border is dual-gauge, but according to EGTRE the standard-gauge track does not see regular use.