Some industries sub-divide themselves by size. Others think of differences of ownership, such as publicly-held, private, or non-profit. However, TPAs tend to describe themselves by the primary type(s) of client. Thus, someone will say they are a Taft-Hartley TPA (with multi-employer collectively-bargained plan clients), or a Single Employer Plan TPA, or Governmental or Church Plans TPA. The vast majority of these types of plans use self-funding.
SPBA-member TPAs normally provide many services . However, there are also TPAs which serve just one particular benefit. Thus, you will find Prescription-plan TPAs, or 401(k) TPAs or Workers Comp TPAs. There are also P&C (property & casualty insurance) TPAs, but it's a very different specialty unto itself.
Pension TPA is not really a separate type, though pensions used to be the dominant service of TPAs. Today, "pensions" is just one of the many possible services, and mostly seen in TPAs who serve Taft-Hartley plans or the many savings plans such as 401(k).
In recent years, TPAs have been called upon to serve all sorts of other plans. Many TPAs are now hired to service fully-insured plans. TPAs are also being hired to administer HMOs and the many variations of provider-sponsored plans such as PHOs & PSOs. Variations of employee leasing are also a market. Important technical/legal note: While there has been lots of innovation of seemingly-new types of plans, it is important to remember that the basic governing laws have not changed, and so do not consider the new types of plans new or separate categories of plans under the law. For example, ERISA recognizes Multi-employer (collectively-bargained) plans, single employer plans, and multiple employer (such as associations). Period. So, due diligence requires that employers, brokers & TPAs make the conscious decision of what kind of plan it is among the existing choices. Employee benefits regulation is not some new frontier without existing rules & limits.