Based on the nature of the investment, types of pension insurance include those that are purely savings plans and those that are investment instruments.
You can also choose on the basis of annuity plans. An immediate annuity plan allows you to pay a single premium and get immediate pay-outs for the rest of your life. A deferred annuity plan enables you to build a corpus over a long period and defer the pay-outs such that they start on a chosen date in the future.
One of the types of pension insurance plans is the Joint Life annuity plan, which continues paying a pension amount to your spouse/partner for their whole life after the primary annuitant's death.