Life insurance terminology shouldn't be confusing. Here is the definition of primary beneficiary.
Primary beneficiary is the person or organization (or persons or organizations, if you want to divide it up) that the insurance carrier will pay first. Contingent beneficiary is the person(s) or organization(s) the insurance carrier will pay if your primary beneficiary is deceased or no longer operating (if an organization).
Make sure your primary and contingent beneficiaries know about your life insurance policy so they are prepared to take action should a problem arise or payout is necessary. For the same reason it's also a good idea to provide them with access to the contract.