Brown trout are caught at sea from fishing boats occasionally. I have caught sea-run browns from the beach while spinning for kahawai far from any river-mouth. I guess rainbow trout would have to be caught in the sea proper to be called true migratory steelheads? Rainbows were often caught in the Waimakariri River just downstream from the bridges in mid-winter. Several old blokes I know used to catch them on shrimps before that was outlawed.