@Jason Bott
Thanks,Jason for the clarification.
My “day job” in addition to real estate investing is in the lending business. My experience has included financing a lot of things people borrow against, including real estate. Here’s what I’d add from my experience - feel free to add or amend as needed.
Additional interest is much the same as “certificate holder”. It confers no rights to you, other than to be copied on any changes, non-payment notices, cancellation notices, etc.
Additional insured is as Jason said - you are an additional named insured on the policy, just like your tenant. You could file a claim against the policy if warranted.
Something else that wasn’t mentioned in the post is what “renter’s insurance” is. Policies may differ. As a landlord, you want them to cover their belongings for their benefit. You want them to also have liability coverage for everyone’s benefit, including yours. My lease requires both (personal property and liability).
I have had agents balk at adding the landlord as an additional insured, citing additional cost, or they “can’t” do it (but no explanation why). I’ve never had an agent objection to adding the landlord as an additional interest. The kicker is just how much risk you are willing to potentially absorb.