Yes, this can be confusing. But you need to realize that some things have to be served in one particular way, while other things must be served in other particular ways. Different statutes have different requirements.
A summons and complaint must be served by personal service as outlined in the statutes providing for service of a summons. A person cannot refuse to take a summons handed to them--they can't toss it back, let it fall to the ground, or something like that--and say they have not been served. Service does not require acceptance.
Service of a summons can be made by mail if accepted. If accepted, the person completes the notice and acknowledgement of receipt for you. The reason they might do that (if they understood the law in that regard) is that failure to accept service then sign and return the notice and acknowledgement, creates a cost shifting. No matter what happens later, if costs are awarded to anyone, the costs of serving a person who refused to accept via mail gets shifted to that person. But no person has to accept mail service--they can force you to complete a personal service or a service by publication or substituted service.
Certified mail is not adequate for service of a summons, so you cannot rely on the cases interpreting serving liens, which can (and must) be served by certified mail. For example, the lien (in the Bear Creek case) was required to be served by certified mail and so refusal to accept a certified mail could not defeat the service. But that rule does not apply to a summons.
I am licensed only in California and this response is provided as general information only. It is not intended to be legal advice. Legal advice must be based on the exact facts of the particular situation, and by necessity this forum is not appropriate for discussion of specific, exact facts. Contact a lawyer for more specific advice. My answer to your question on AVVO does not create an attorney-client relationship.
It sometimes depend on what you are serving, but generally, summons and complaints need to be personally served.