A "working interest" is the leasehold interest acquired by an oil and gas lesee from the lessor (mineral interest) owner pursuant to the terms of an oil and gas lease.
In the absence of co-ownership of the working interest the concept of "operating" or "non-operating does not come into play.
It is only when the working interest is held jointly, and thus the need for a Joint Operating Agreement to be executed by the parties, does the concept apply. The JOA is a contractual agreement which sets forth the parties, rights, obligations,etc. in regard to how the property will be developed and expenses shared--typically pro rata in proportion to ownership.
Normally, the party owning the largest percentage of the working interest will be appointed as "Operator" under the provisions of the JOA. An operator's duties are a function of the powers granted to it in the JOA. Typically, the operator will propose wells, maintain the joint account and are resposible for joint interests billing (JIB's).
There are both advantages and disadvantages of holding operated versus non operating interests. For example, the Operator will select the various service providers on wells, and it is common for non-operators question the cost effectiveness of such selections. Non-operated interests typically are much acquired by smaller independents because their pro rata share of expenses are netted out of production, thus mitigating the capital requirements necessary for participation in the development of the oil and gas interests.
There are tons of other factors which come into play in answering your questions. I hope this helps.