Your use of the term "downloaded" is vague and ambiguous. Sounds to me like you're using it to describe a complete process, rather than just one step in a multi-step process which is what that word actually should be used for.
Sounds like you're trying to write a complete tutorial for ALL THE STEPS (of which there are MORE THAN ONE) needed to get a vendor product from the vendor's web site to become operational on your own computer, and that includes "downloading the installer file" as just the first step.
The word "download" itself really describes the first step in the process, when you click on the typical DOWNLOAD button on the vendor's web site which initiates your browser to actually want to transfer the installer file (e.g. SETUP.EXE or something like that) from the vendor's web site DOWN to your own computer somewhere. If you haven't done any setup regarding "downloads" in your browser, the usual default target location for receiving any similarly downloaded files is in the \Users\<username>\Downloads folder, from where it can then be installed or further moved to a more appropriate permanent location on your hard drive somewhere.
Now depending on whether you explicitly or implicitly specify the target location for this "downloaded file", you may or may not get a popup message about "duplicate file exists with same name, do you want me to replace it". So in this sense, yes, you may or may not get a message the second or subsequent time you try to do this first preliminary "download" step vs. what you saw on the very first time. But it's not terribly significant.
Once the installer file is actually downloaded from the vendor web site to your PC's local hard drive somewhere, you then RUN it to actually "do the installation of the software into your \Program Files" folder and create Start Menu shortcuts to launch it, etc.
This step is referred to as "installing" or "running the installer file", rather than the earlier "downloading of the installer file" just to get it onto your hard drive somewhere from which it can then be RUN (or "the software represented by that installer file actually getting installed onto your PC".
And now the answer to your question about whether or not there is any harm or difference in "running the installer file a second time", well that depends on how the vendor packaged the installer file in the first place. Some products just run the second and subsequent time completely oblivious to how they ran the first time, and you'd never know you already had previously installed the product. Some products treat every "second" run of the installer as a request to either (a) repair or (b) uninstall or perhaps a request to selectively install/uninstall optional features you overlooked or previously installed.
Furthermore, some products will recognize the previous installed and customized versions of themselves, as either the same or earlier version, and perhaps will make use of whatever customization and data you've previoulsy established for the product in the installation of this latest version of the same product. Others will simply disregard what you might previously have customized, and just hard put you back to the program's initial state.
So it's hard to predict what differences if any you might see when you "run the installer file" for a second or subsequent time. Depends on the product, and only you would know that from your own experience with this product.
All in all, if you're trying to write a usable and accurate "tutorial" describing all steps A-Z for how to get a product DOWNLOADED from the vendor's web site until it is fully INSTALLED and operational on your own computer, and then how it might be CUSTOMIZED once installed, and then how it might be UNINSTALLED if no longer wanted, you tutorial must be precise and accurate in its terminology.
Furthermore, it must recognize and describe EACH OF THE ABOVE STEPS SPECIFICALLY AND INDIVIDUALLY.
And the use of the word "download" truly has a very specific individual and precise meaning, and that is NOT a generic one used to describe the entire multi-step process... each of which has its own single word to describe that one single step in the multi-step process, of which "downloading the installer file" is just the very first one.
And to be truly helpful and complete, any "installation guide" should provide (a) examples and screenshots/pictures, as well as (b) exhaustive discussion of ALL THE OPTIONAL RESULTS which might occur at any point which produces multiple optional results, depending on conditions.
That's my take on it. Hope it helps you with your writeup.
