If you use the internet, you already use Free, Libre (It's French for free, don't ask) or Open Source Software. Popular Web Browsers Chrome, and Firefox, are based on it.
Your home router probably uses Linux with Busybox; as for your Android phone, your website, and if you have devices connected to Apps on your phone or computer, they are almost certainly based on Open Source Components.
More than any other domain, web development is dominated by open source components. Companies like Facebook and Google (and even Microsoft these days) have open-sourced a number of projects from new computer languages (Go Lang, Typescript, Rust, Python) to development frameworks like Angular, or React.
These and many other elements like them can be used by a developer as the components for a "System Architecture" to do something useful, like getting your new Customer Relations Management System (CRM) to talk to your legacy Market Research System.
"Free Software" and "Open Source Software" are software released under licenses that guarantee a certain specific set of freedoms. Open Source licenses are licenses that comply with the Ten Point Open Source Definition — in brief, they allow the software to be freely used, modified, and shared.
Free Software is licensed under the Four Freedoms of the Free Software Foundation, wi state that “Free software means software that respects users' freedom and community. Roughly, it means that the users have the freedom to run, copy, distribute, study, change, and improve the software. Thus, “free software” is a matter of liberty, not price. (see http://www.gnu.org/philosophy/free-sw.html )
One thing I know is that while our Geekforce gets very exercised about some of these subtle differences, you and I don't have to. It's a bit like the People's Front of Judea, and the Judean People's Liberation Front from Monty Python's Life of Brian.
Like the FSF, the OSI's founders supported the development and distribution of free software, but they disagreed with the FSF about how to promote it, believing that software freedom was primarily a practical issue rather than an ideological one. Confused? Think of the FSF as the OSI's hippy older sibling, and you get the idea! Unsurprisingly, the Open Source Initiative's pragmatic approach lends itself to business use.
While some of the rhetoric on both sites can be pointed, the key issue for both is that the Source Code remains freely accessible and able to be modified or improved. One of the concerns often cited by adopters of the term "Open Source" is the ambiguity of the English word "free", which can refer either to human freedom or to mere monetary price; this ambiguity was also given by the OSI founders as a reason to prefer the new term.
Importantly, while many Open Source AND Free Software components may, indeed, be available without cost, either, or both can be incorporated in software that is then sold commercially. So, "Free as in Speech, not Free as in Beer".
And Libre? (I know, I said "Don't Ask"). It's French for Free (as in Speech). But mostly it just makes a better acronym!
Today people use both terms, often interchangeably, sometimes choosing according to context and audience, and, for most intents and purposes, Software developers may use code issued under both licences.
Because this is a licensing issue, there are some legal niceties, so your best bet is to go with Developers who specialise in, and are experienced with FLOSS, who can spot the pitfalls, and recognise the occasions when further advice should be sought.
As long as your Developer knows which licenses to use in which circumstances, the difference remains one of approach for the consumer.