The primary retirement account type for employees of non-profit organizations including schools, libraries and hospitals is called a 403(b). The 403(b) structure is what provides the tax deferral of contributions under the Cash or Deferred Arrangement rules. For those who work in businesses the 401(k) structure is the equivalent type of account.
It's been nearly 50 years since the 403(b) was born and early on "annuities", which are contracts issued by insurance companies, were the only available investment option. A lot has changed over the past 5 decades including the investment options available in 403(b) accounts, but the account is still quite often referred to as a Tax-sheltered Annuity (TSA).
How do you know whether you're investing directly into mutual funds or accessing them through "sub-accounts" in an annuity? First, if the company you're investing through is an insurance company there's a pretty good chance it's an annuity structure. Second, check to see if you own "shares" or "units". If it's the latter, it's definitely an annuity. Lastly, look for the words "contract" and "surrender charge". These are telltale signs you're in an annuity contract.
Why does it matter? In a word the answer is cost. Annuities generally have higher cost than mutual funds. While there may be features an individual is specifically seeking in their account such as a guaranteed death benefit, most often they are just not aware of the differences or the fees they are paying.
When saving for long term goals like retirement, fees really matter, so familiarize yourself with your retirement plan options, ask questions, stay informed.