Not really, no. An LLC must register with the state by filing the proper documents, usually with the secretary of state. But the rights of the members, or even the sole member if it is a one member LLC, are established in the LLC Agreement or Operating Agreement that the member or members sign when the LLC is formed. If the member ot members do not adopt such an agreement, then their rights are dictated solely by state law "default" provisions, which may or may not be right for the individual company.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
Probably they are not the same thing. "Forming" or "organizing" are typically the terms used to describe the set of filings that bring the LLC into being. The LLC is "formed" upon the filing of Articles of Organization with the Secretary of State (or similar body) of the state of its origin.
"Registering" is frequently the term used for qualifying an LLC to conduct business in another state.
For instance, an LLC formed under the laws of the state of Utah may want to engage in one or more transactions in the state of Georgia. The Utah LLC would "register" with the Secretary of State of the state of Georgia prior to engaging in business here.
Sometimes an LLC's annual renewal of existence filing is referred to as its annual "registration," too.
The foregoing is not intended to, nor does it, constitute legal advice or establish an attorney-client relationship. The author is licensed to practice only in the state of Georgia. No reader should rely upon the foregoing and should seek independent counsel.