@iEllaLouise - I can understand your confusion, and you do have a determination to understand more about the difference between the achieve vs gaming machine.
One of the things to keep in mind is that we need to avoid 'a bit too much' reductionism. IOW, it seems like the components making up each of the machines seem ideal in different ways but it's actually the composition of the WHOLE computer that really makes the difference.
The Curry's site is about marketing, you don't see details like how each build is created to manage the hardware with different installed firmware that goes with the installed motherboard and more expensive memory modules and so on. There's no information on the motherboard and other such hardware at most markets. Think of it this way: It's like buying 25 dollar copy of a 5000 dollar designer dress. The computers are made up of many different components and software aspects that are targeted to a specific consumer group. And this is the stuff that will throw you into serious tech disadvantage. It's beyond what we can cover here.
So if Curry's and HP are aiming at the the gamer population, they will show that a machine is directly targeted toward that specific population of consumers. Beware there are low end, medium and high end gaming machines. Some low end machines will play a game (for a while) but the user experience and (in)stability may differ greatly with reportedly included hardware. (I'll say this now: I'm no fan of HP's lineup for reasons having to do with reputation of HP in the GAMER community -- and among those who repair said "gaming machines" -- for HP machines tend to be overrepresented.)
One way to compare machines and learn more about particulars, is to take the official name(s) of the computer(s) and enter it into your own internet search template (a template which you should modify for your own use)-
'machine1 vs machine2' (reviews)
-be aware that this is just a template and what comes up in the search may not even be the computer you are researching.
And finally.
Logging into websites can be an issue regarding clearing cache (your first step usually) and also trying a different browser.
For Tomshardware specifically, Why not do a search for ideas, using something like:
Tom's Hardware login issues
When you are actually ready to make a choice in a gaming computer, that is the time to consult these forums. The hardware in the computers being sold now may change drastically in as little as half a year or less. Good luck!