The question is as the title says: what is the difference between A/B Testing and Randomized Control Trials?
A/B testing seems to be computer geeks terminology, but the idea is of course same. You have an control version of web-page and changed one and you test if difference between some user action rate is statistically significant between versions of pages.
A/B testing tests single feature combination differences when multivariate testing tests different combinations of their interactions.
As @Analyst (+1) says the basic idea is the same; A/B tests and RCT refer to the same notion.
What is interesting to note is that while in the past the methodological advancements/notions have been primarily a one-way street from RCTs to A/B tests, i.e. from "medical statistics" to "online marketing", lately there have been works in the opposite direction. Obviously, this is partially fuelled by the extensive investing online retailers have on the field; nevertheless a lot of healthcare nowadays has a clear electronic footprint too (wearable sensors being the most obvious example). To that extent, I think that some issues like violations of SUTVA were more aggressively explored by online retailers than healthcare practitioners, as network effects have such a prominent influence in online behaviour. Similarly, some of the most involved and high-value inferential tasks like that of Heterogeneous Treatment Effects (HTE) estimation directly translate to industry goals of personalised marketing and precision medicine respectively. Thus allowing a lot of learnings being transferred from "online marketing" to "medical statistics".
Two prominent papers on this matter are Kohavi et al. (2020) Online randomized controlled experiments at scale: lessons and extensions to medicine and Austrian et al. (2021) Applying A/B Testing to Clinical Decision Support: Rapid Randomized Controlled Trials. Both papers are very insightful, easy to read and help make this functional equivalence between the two terms more clear and well-defined.