Does the latest version of ColdFusion Standard allow multiple (hundreds) of concurrent websites?

Kindred, so let's be clear: you are asking if CF can handle multiple hundreds of web SITES, not users (though that can be implied also). And you ask if there's a change from CF8 to CF2018 Standard that may affect that.

First, you don't say if the CF8 was Standard or Enterprise. That could be helpful to know.

Second, on the surface, no, there's no reason to think or assert that somehow CF 2018 Standard can't handle "multiple  hundreds of web sites", if CF8 was able.

Then again, I'm sure you're moving from an old box to a new one, right? And probably from an old OS to a new one, right? And perhaps even updating the DB you use? And of course your web server version will likely change. Was it Windows and IIS? Linux and Apache? or some other combination?

I ask all this because ALL these factors could just as readily lead you to find that your "move" fails--but not because of CF, so do be careful when trying to understand when things might go amiss. It's easy to blame CF.

Now, back to the question of whether CF8 was Enterprise or Standard: if it was Enterprise, and you are moving to CF2018 Standard, there's no aspect specific to that change which will make it that new CF implementation can't "handle as many web sites". But there is an aspect of that which may affect whether it can handle "as many users".

CF Standard differs from Enterprise in at least one key matter that relates to that: Standard implements something called the "enterprise feature router", by which CF essentially single-threads access to certain tags, like cfdocument (for creating PDFs) and some more. What this means is that while ONE request is processing a CFDOCUMENT, no OTHER request that wants to use that tag will be allowed to run, until that first one completes. Often there's no problem, but if ever a given CFDOCUMENT hangs up, and other frequently run requests want to ALSO use that tag, that can suddenly make CF seem to be "hung up", if all available request threads (set in the CF Admin "max simult requests" setting) get used up waiting on that CFDOCUMENT.

But back to the question solely of SITES, no, there's no difference in CF Std or Enterprise (or 2018 vs 😎 about how many "sites" CF can handle. Of course, such sites are setup in the web server (like IIS or Apache), and then CF is connected to those sites (with the wsconfig tool, which looks nearly identical in CF2018 to what it did in CF8). But there is no limit to how many "sites" CF can be configured to run.

I WILL note, however, that since CF10, there is a change in CF with respect to how that web server connector configuration works. There is a new need to properly TUNE these connectors (especially for use with IIS, but also with Apache). There are two key factors: one being how many sites use a given connector (in terms of some settings in a workers.properties file for each connector)--and then also another need to configure a CF setting relative to how MANY connectors there are and how they are configured (in terms of a maxthreads setting for the AJP connector within the server.xml file). 

In CF10 and 11, the default settings for these things basically only suited a single-site setup out of the box. And in CF2016 and above, the defaults are confgured to suite a two-site setup. Once you have many sites using a given connector, or of you decide to create many connectors, then there are very different settings that are needed. This info is covered in a blog post that Adobe shared back in 2014, relative to CF11. The info shared then is as relevant today (in 2016 and 2018) as then, other than this change in the default values. You will want to read that blog post (which is a bit of a mess, sadly), as well as some of the many comments that were shared. It's here:

https://coldfusion.adobe.com/2014/05/coldfusion-11-iis-connector-tuning/

Or I will say that if you have trouble deciphering it, or setting things up, I can help do it, on a consulting basis, remotely, and any day this week or in weeks to come, if you'd like such help. More at carehart.org/consulting.

Or you can ask questions here, and others may well chime in with more info, whether on things I shared or still other matters for you to consider. Hope that's helpful.