As others have stated, you have either a "A" grade (damascus barrels), or "B" grade (twist) barrels.
Baker double barrel trap guns are quite rare and are typically higher in grade than a Paragon. Of course they made "A" & "B" grades and others with tight chokes and longer barrels that could used for trap shooting.

Billgrill - The straight grip Trap Gun is offered in the 1904 catalog. This model was only offered for a few years.

Chris