Sweden and Finland were two parts of the same country until 1809, when Finland was ceaded to Russia. There has. therefore. been a continous migration between the areas before that war. 'Celebrations' in both countries this year!!
But three major migrations may be mentioned
1) Finns from eastern Finland (Savolax) moved to Värmland in Sweden in the 16th century to build new farms (a little too early?)
2) During a war in the 1720:s many 'Finns' from the higher classes fled to Sweden, many remained in Sweden
3) I suppose the same thing happened in 1809, but there has been little information as to migration. Finland continued to use the Swedish governmental system and Swedish laws of 1634.
I suggest that you look for English-spoken web-sites on migration in Finland, or contact
www.genealogia.fi (choose language English)
By the way, from Savolax people migrated to Fort Christina. Pennsylvania. One of them was a Juhana Matinpoika/Johan Mårtensson, known by the name John Morton, one of those signing the Declaration of Independence.
Good hunting!