I just discussed that in another thread a little bit ago, but can't find it. In short, they are basically, but not quite, synonymous. Here's an explanation from another post I penned some time back:
" The simplest way I know how to put this is that infection is the growth of an organism within a host or the introduction of such to a host, which may be counteracted by antibodies, and not necessarily become disease, and disease -- which infection can lead to -- is what happens when and if that battle is lost and the organism essentially changes the host.
Thus STIs are infections, STDs diseases. For example, HIV is an infection which can lead to AIDS, which is a disease."
But "disease" is also often used as an umbrella term for illness as a whole.
Many people tend to use "STD" as either a scare tactic or with a plotical agenda to stimgatize, because many people find the term "disease" scarier than the term "infection."
Medically, STI is the most recently accepted umbrella term, if you choose to only use one, and most STIs/STDs ARE specifically viral, bacterial or parasitic infections, so it's the most accurate. We often still use the term STD mainly because some people are more familiar with it.
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