The system described here is basically standard CFOP: Cross, First 2 layers, Orient last layer (OLL), Permute last layer (Pll). Though now most cubers don’t take advantage of the symmetry between algorithms, and instead do completely different algorithms for flipped cases. One reason for this is that most people aren’t perfectly ambidextrous, and the other is it can facilitate recognition.
The second most popular method, Roux, has also a lot of potential. Completely different from CFOP.
CFOP has been refined a lot. First the obvious: the cross is solved at the bottom, and so are the first two layers. That way you can better see the pieces that actually interest you: those that aren’t solved yet. And it saves you from flipping the cube over when it comes to solve the last layer. The first two layers are still solved mostly intuitively, but with a lot of tricks to make it faster, like pseudo slotting, key-holes… currently Tymon Kolasiński is the master of pseudo slotting, with extremely efficient F2L (and standing equal to him is Max Park, who is basically ambidextrous for this phase).
For the last layer there are also a lot of tricks, most of which requires recalling an ungodly amount of algorithms. Some are about inserting the last pair and orient the last layer (few cubers learn them all, but the set called "winter variation" is fairly popular). Sometimes the edges are already oriented, so we can orient and place the last corners (COLL), so at the end we only need to permute the edges (easier recognition, slightly faster algorithms than general PLL).
And then there’s ZBLL, from the ZZ method, where we start with edges already oriented, and we orient the corner and permute everything in a single algorithm. But there’s a crapton of algs to learn from, not even Tymon Kolasiński knows them all… well, one cuber does know them all (don’t recall his name, sorry), I believe his method to solve the last layer is to orient the edges at the same time he places the last F2L pair, then he goes ZBLL.
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If you want to learn speed cubing now, I recommend https://cubeskills.com/ and https://jperm.net/ — or look up the Roux method if you don’t want to do like everyone else.