You sure are going about this in a strange way. It's like seeing a house you like, wanting to build a similar house, and you start by asking what tools the builder used!
Using the same brand of saw and drill aren't going to help you much in building a similar house, if you don't know anything about building a house. Nor is it going to help you if you are delusional about the effort needed to build a house, and think that it will happen by magic and take almost no time, if only you use the same tools as the builder. And, oh, you've also seen an informercial about some magic tools, that will allow you to build your own house for free in just no time! YES, you want to use the MAGIC TOOLS, not the ones that most builders use, and certainly don't want to take any time or effort to learn how to build a house! All, that, and you want the magic tools for FREE!
It could happen! But you may have to wait for the upcoming Dreamworks Felix the Cat remake. Perhaps there is a magic web designer in his Magic Bag of Tricks!
But you will have to pay the price of a movie ticket, or else wait for it to come on broadcast TV.
Is there something free i can experiment with that can achieve a result just like the A & B examples?
Yes.
A text editor and a browser. Both come free with your OS.
Though, I'd suggest at least a separately-downloaded, free, programming-oriented editor.
As well, you will need to use the browser to look at instructional sites, and teach yourself HTML, CSS, and Javascript. And perhaps some server-side technology, such as PHP, Rails, node.js, Python, etc. etc. (take your choice).
I believe there are "free" "site-builders", similar to SquareSpace. But they will load your site up with ads that you have no control over and that the host gets revenue from. You can't expect such a service to really be free. And, frankly, they are probably all just lousy, inadequate, truncated copy-cats of SquareSpace, Wix, etc.
Instead of asking what tools were used, you should explain what it is you are trying to create, and ask what you need to learn to do something similar. Explain what it is - don't just point to some example site and ask how to make a page like this - it's a rather meaningless exercise.
For example, you haven't explained - do you want to make some kind of ecommerce site (are you selling something) or do you just like the grid layout? Do you need a database of products that will be fetched from a server? Do you need an ordering/shopping-cart system and payment ability?
Frankly, if you know nothing, you either need to hire somebody, or be willing to spending an awful lot of time and effort learning. You will not find something that will do it for you magically, let alone for free. (You will find plenty that will CLAIM to do it magically, and will charge you for it!)
If you are willing to spend a great deal of time and effort learning, I would spend it learning the fundamental technologies - at least HTML, CSS, Javascript - rather than wasting your time learning the intricacies of a closed system like SquareSpace.
As for "making a site like A", you can do it by literally copying the A site files and then hacking away at them in your text editor.
BTW, my preference is SublimeText. But it is not free.
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Most of the lot? What others are out there?
Use the Google, Luke! I mentioned another popular one - Wix. There are many.
What do you mean by escape hatches?
The ability to bust-out of their little drag-and-drop universe and integrate your own custom HTML, CSS, and Javascript, when you find that their pre-packaged solutions don't exactly fit your need.
I don't understand the disadvantages, can you be more specific please?
The ability to "export" your work is limited. If you decide you don't like your host, and want to move somewhere else, it will be difficult. You can't just move the site as-is, as it is built in such a way that it is very dependent on their proprietary bits and pieces.