Does getting added as an authorized user on my relative's higher tier credit card (with an annual fee and better benefits) have a different impact on my credit score when compared to getting my own secured credit card?
Many credit card companies report authorized users to credit bureaus, but not all do. If they don't, your credit won't be impacted by being an authorized user. Check with your relative's card company to be sure. But assuming being an authorized user does go on your credit report:
Your credit can be positively impacted by continued on-time payment history by your relative. However, if they miss a payment, your credit could be harmed even though they (as the primary cardholder) are solely responsible for making payments.
High utilization of the card (as a percentage of the limit) can also hurt your credit, although this is generally much more temporary since reducing utilization has a pretty immediate positive impact. However, you won't be able to control the utilization percentage as an authorized user the same way you would as the primary or only cardholder.
In the long term, having your own card could have a more positive impact if your credit card company retains your account history when you eventually switch from a secured to an unsecured card. Length of credit is a substantial portion of your score. On the flip side, if you're removed as an authorized user on someone else's card, you may see a drop in credit score when the credit history drops off of your report (generally 10 years after closing).
The annual fee and better benefits (miles, perks, cashback rewards, etc.) shouldn't impact your score.
Your own personal credit card would be better, IMHO, since you won't depend on someone else's behavior. While having a higher tier card means they're probably reasonably disciplined, it's still a risk.
On the other hand secured card requires a deposit and will come with lower credit limit and potentially fees, but that's temporary and may not be such a bad thing if you're just starting building your credit.