"open source is like throwing something into the public domain?" - No
"is there a difference between works classified as open source, and works in the public domain?" - Yes
"What's the difference between the two?" - The short answer is that open source requires agreement to a license, Public Domain is without restrictions. However, because the term Open Source is misleading here is my perception on the issue.
Like most of life (and law) open source is not a binary yes or no, but can fall between the two depending upon the individual circumstances of the software/product/license/terminology combinations. The resultant fuzzy logic licensing of a complex project that pulls resources from multiple sources can result in much heated debate. I think of rights to using software code as sitting on a sliding scale. At one end is propriety software from a commercial organisation that keeps source code hidden and secret. At the other end is source code out in the wild that has no restrictions upon it at all, free to be used/changed/abused by everyone, this is software in the Public Domain. You need to slide the scale back a little for open source. How far the scale is slid back depends upon the particular licence. A bit for the MIT licence, a bit more for the GPL licence. It can be slid almost back to the beginning where source code is licensed as open for viewing and nothing else, no changes whatsoever, why? Just to see how it works and for interfacing purposes. This is not uncommon in industrial systems.
Open source is mainly about source code, however, software can be in the Public Domain but the source code is kept secret (e.g. a programmer waivers rights to a little utility but keeps the source code under wraps). Furthermore time will eventually start contributing to Public Domain software. Once enough years have passed software falls out of copyright and becomes Public Domain. (Open source licenses then lapse.) When that happens the source code no longer needs to be readily available for the compiled files. Thus, perversely, in the very long run, this could cause beneficial changes to source code not being available.
The issue of what it means to have free rights to the software is often misunderstood. The free is about freedom of expression, not cost. Some misunderstand this and think open source is free of cost. Open source software can be sold, as long as the code comes with it (though the purchaser is then able to provide the software without selling it). This is also why open source software can be sold on disc media, mainly to cover the costs of production and distribution. Again perversely once the software is in the Public Domain there is nothing stopping organisations from modifying/renaming it then selling the product and not releasing the software's source code.
So open source is mainly about freedom of expression, but need not be, and is not in some cases. Public Domain is about freedom in all senses, expression and cost, but that may lead to software becoming less free. One reason why the term Open Source is disliked by some is that it is misunderstood and misused. If you want true freedom of expression in software then open source is not an appropriate term. Nor is releasing it into the Public Domain (waiving all your rights). Hence the GPL license is probably the most free licence. Though some perceive it as restrictive, but strangely it needs to be to allow for full freedom of expression.
I would consider "freedom software" as a proper term for truly free open source software (GPLed). Unfortunately "open source" dominates and as an umbrella term that is not truly free software.