The main difference between a Gift subscription and a Prepaid subscription is that the gift has a voucher. Though both subscriptions are for a pre-determined amount of time, the gift subscription starts whenever the voucher is redeemed. When a gift recipient redeems their voucher, they set up an account for themselves with their email and address.
Another difference is that Prepaid subscriptions renew automatically at the end of the term once they are completed. Gift subscriptions do not renew.
Finally, prepaid subscriptions are set up for half a year (26 weeks) rather than 6 months whereas Gift subscriptions are set up for 6 months, assuming 4 weeks every month (24 weeks).
To summarize, if you are buying for yourself and ready to commit for 6 months, get a Prepaid subscription and if you are buying for someone else, get a Gift subscription.