A single life insurance policy covers one person. When that person dies the policy will pay out a lump sum to their estate.
If a couple buys two single life policies, the policies will be completely independent of each other. The two policies can be underwritten by different life insurance providers, for different terms, and each policy holder can be insured for a different amount. Each policy will pay out only when the policyholder dies.
You may want to read: What is a Joint Term Life Insurance Policy?