Yes, the type of procedure done may be very different, as the causes of ptosis are likely to be different.
In an older patient, the ptosis is more likely to be due to stretching out or thinning of the levator muscle attachments. This can usually be corrected by re-attaching the levator muscle which will restore function.
In very young patients with congenital ptosis, muscle function may be very weak and may require different procedures, for example static or dynamic slings which recruit the help of other muscles to improve eye opening.