Ship leaving Glasgow

[bzquiltn]

HELP! My grandfather and his family came to the US via a ship from Glasgow, Scotland. However, it is my understanding that they were not Scottish, but possibly English or Irish.
Are there any records that I can check to see where they were living or where they orginally came from? My great aunt's immigration information into the US said she was born in Glasgow, Scotland, but we pretty much know that not to be true, as we've also found a copy of her birth record and that was in Ireland!
ANY help will be greatly appreciated.
Diane