I don't know about Scotland, but in England, a short birth certificate for an adopted person has different wording on the printed bit.
A non-adopted person's says "I [name of registrar] Superintendent Registrar for the Registration District of .......... do hereby certify that the above particulars have been compiled from an entry in a register in my custody."
An adopted person's says "Certified to have been compiled from records in the custody of the Registrar General. Given at the General Register's Office, Somerset House, London under the seal of the said Office on the ..... day of ..... 19xx."
So, if you don't know what you're looking for, it would be easy to miss the difference.