tl;dr - outside of a specific medical context, scholarly publications describe the term "sterilizing vaccine" including in online forums, as a FUD term by anti-vaxxers.

walterbell previously used the term "sterilizing vaccine", and at https://news.ycombinator.com/item?id=28883691 commented "There's a stable definition in textbooks." / "If 2021 consumer media is offering variable definitions, Cui Bono?"

I decided to investigate.

Google Scholar reports about 176 uses of the phrase "sterilizing vaccine"; the infrequency suggests it is not a common phrase, especially given how it's sometimes given in quotes, like:

> Because of the ability of HIV to rapidly establish latent reservoirs and undergo immune escape, it has been proposed that an HIV vaccine will need to be a “sterilizing” vaccine, or a vaccine that prevents infection in the absence of an anamnestic response. To achieve sterilizing immunity, a vaccine needs to elicit persisting levels of Ab that are sufficient to block an incoming infection. - https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4019109/

Most of the references to "sterilizing" were either regarding HIV, or recent publications about COVID, but not all. Here's one for chlamydia:

> The holy grail is to produce a sterilizing vaccine that would completely prevent infection in the individual and hence also prevent transmission of infection to others. However, if 100% prevention of infection is not possible to achieve, then some consideration needs to be given to a vaccine that mainly prevents ascending infections that lead to disease pathology. In fact, one argument might be to focus on the disease pathology, as this is the major consequence of infection. - https://www.sciencedirect.com/science/article/pii/S0264410X1...

Do note that "sterilizing vaccine" is also used to describe (putative) sterility caused by vaccines . This is not some sort of recent '2021 consumer media' definition.

One is the 2008 publication "Sterilizing Vaccines or the Politics of the Womb: Retrospective Study of a Rumor in Cameroon" concerning "a rumor that public health workers were administering a vaccine to sterilize girls and women" - https://anthrosource.onlinelibrary.wiley.com/doi/pdfdirect/1... . Another is https://www.taylorfrancis.com/chapters/edit/10.4324/97813151... , also about the same rumor.

A third is "HPV Vaccine Representations on Online Discussion Forums in Romania" from 2013 :

> A subcategory of people postulated that the vaccine is promoted with the hidden intention to exterminate part of the population: “Some guys out there consider we are too many on this earth!…They want us dead.” (NS, 2009). They frequently mentioned words such as “genocide”, “Masonic vaccine”, “experiment”, “sterilizing vaccine” and they considered vaccination as “the biggest crime against humanity”.

A fourth is https://dergipark.org.tr/en/download/article-file/275883 about reasons for why heads of family decide to not vaccinate their children against polio:

> Aşılamaya uyumsuz aile reislerinin OPA’nın ilk dozunun ne zaman olduğunu bilmedikleri, OPA’nın güvenli olmadığı ve infertiliteye sebep olabileceğine inandıkları gösterilmiştir (1). - https://dergipark.org.tr/en/download/article-file/275883?_x_...

[Translation] "It has been shown that heads of families who do not comply with vaccination do not know when the first dose of OPA is, and they believe that OPA is not safe and may cause infertility (1)."

(This cites the Cameroon paper as previous precedent.)

And one is a non-scholarly report from the Baker Institute AnnualReport 2011-2012 on a vaccine to make dog sterile:

> The dream of a long ­term solution to pet overpopulation has remained unreal­ized, ... "Dogs are so reproductively efficient that it's hard to make an impact with spaying alone. A safe sterilizing vaccine for both males and females could rapidly reduce feral dog populations and significantly improve their wel­fare worldwide." - https://ecommons.cornell.edu/xmlui/bitstream/handle/1813/482...

Thus, it seems best to avoid the terms "sterilizing vaccines" and "non-sterilizing vaccines" 1) in a non-clinical forum, and 2) in a context where the more specific term adds nothing.