You obviously are a bit clueless on this. Legally, only licensed life, accident and health insurance companies can issue annuities.... annuities are a subset of life insurance since they need to have elements of mortality risk to qualify as annuities for tax purposes... yes, even your plain vanilla fixed rate SPDA that looks like a CD has mortality risk because of annuitization options in the contract that rarely get utilized... that is what makes the inside build-up tax deferred.
TIAA is a huge, very well known insurance company that sells a wide variety of insurance and annuity products.
Vanguard is an investment company and is an agent when it sells annuities.... the fixed annuities that Vanguard sells through a relationship with Hueler Investment Services are issued by insurance companies like AIG, Integrity, Symetra, Lincoln and Mutual of Omaha... the variable annuity that Vanguard sells is issued by Transamerica and administed by Vanguard (much like Vanguard administers 401ks).
You're right.. I don't know much about Vanguard and TIAA annuities and how they are issued. My point is that an investment focus company have to be looked at closely on what their objectives are. Also in your example, Vanguard using an agency to sell their annuities proves my point that the marketing has to be paid to somebody .. in that case Vanguard and Hueler are sharing it. Your job as someone seeking a benefit is compared the Vanguard annuity vs anything else in the open market .... which one offers you the benefit you're looking for.