Certificate holder
The certificate holder box on a certificate of insurance identifies who the certificate was issued to. Being named there means the holder receives the document and, if the policy carries a notice endorsement, may be notified of cancellation. It gives the holder no coverage, no rights under the policy and no ability to make a claim.
Additional insured
An additional insured is added to your policy by endorsement. For claims that arise from your work or operations for that party, the additional insured is defended and indemnified under your policy, up to its limits, as if they were an insured. That is what landlords, general contractors, franchisors, venues and clients mean when their contracts ask for it.
Why both appear in the same request
Contracts ask for a certificate so the other party has proof, and for additional insured status so the other party has protection. A certificate without the endorsement proves you have insurance but leaves the other party exposed; the endorsement without a certificate leaves them unable to show their own insurer or lender what exists.
How to check which your policy provides
Look at the forms and endorsements list on the declarations page. Additional insured endorsements have form numbers and titles that say so. Blanket forms refer to parties "when required by written contract"; scheduled forms list the parties by name. If no additional insured form appears, the policy provides none regardless of what a certificate says.
Ongoing versus completed operations
Construction contracts split additional insured status into two: for work in progress and for completed work. The second matters more, because most construction claims arrive after the job is done. Two endorsements, or one combined form, are needed to satisfy both.
The practical test
Before a contract is signed, hold the insurance exhibit next to the forms list on your dec page. Each additional insured, waiver and primary-and-non-contributory requirement in the exhibit should have a matching form in the list. Where it does not, the fix is a quote for the endorsement, not a note on the certificate.