Lol, it sounds confusing!
CFBS is giving you examples of VOCATIONAL qualifications. They generally take longer to complete, cover a whole range of related topics and are universally recognised in the industry by all brands, insurers and employers. This is what I went for so I get to fast track through other training and/or gain immediate access to most pro only suppliers.
Then you can get Academy training which will get you a certificate issued by the particular academy you attended which is usually supported by one or another insurer who you can then get insurance with. These may or may not be considered proof of your training standard by different brands, so you might still have to undertake their full training from scratch when you decide to work with their products.
Alternatively if you are only interested in offering a particular brand... say CND for example, you can take your training directly with them. Once completed you can provide CND services specifically and get insurance for that in particular. There are many brands to choose from who provide such training and often the fee includes a starter kit.
Which route you take depends on what’s available in your area, what your budget is, how far you are prepared to travel and how much time you have available.
I’ve not mentioned on-line training as I don’t know much about that option.