I guess I see the distinction, but the assumption there is that you are always making decisions based on incomplete information, so buying something else is taking a chance on the unknown. This is much less often the case these days with the abundance of ways we have to research products, such that choosing to buy something based on brand alone is more of an overt rejection of other factors.
Brands grew to prominence with the advent of mass production. Prior to that, goods were produced locally for local consumption and you were at the mercy of local vendors as to the quality of wares and goods you got. An example is confectionery, where some Victorian confectioners would put sawdust as a filler into their sweets. A product founded on the best quality and communicated as such meant you could make an informed choice - buying Cadbury's chocolate meant getting proper, quality chocolate without having to worry about unwanted ingredients. After a while, companies found that they could influence consumers by working on the psychological associations with the brand name rather than the product itself. Hence we see a move away from explicit advertising of a product's qualities to the subtler modern advertising where it's more about image and association with cool looking, happy models and celebrity endorsements etc.
Brands are therefore psychological connections, like any other. You'll get some people hooked, like a cult (will die to protect). You'll have others enthused, like a religion (will resist change, but sufficient reason to change can cause them to change beliefs). You'll have some in favour, like a club (you may visit a club routinely, but you won't shun other social opportunities and may replace it). And some who don't have any psychological preference (there'll of course be anti-loyalty, or Brand Prejudice, though I've never heard that talked about explicitly).
There are far too many considerations to be able to make proper informed choices for every product we buy, so we have to rely on other things. Take the Beats headphones example. There are dozens, if not hundreds, of headphone options for a potential customer. The effort to research all of them and find the best ones is not insignificant. Seeing everyone else walking around with them takes the pressure off, because the Masses must know something you don't, and if they all know these headphones are the ones they want, they must be the best... That's where user reviews have picked up, where we can see at a glance which products are recommended by one's peers. Seeing as these can be cheated and, quite frankly, the quality can often suck ("5 stars! I haven't used it yet but it looks good."), I expect personal filters for these are going up in users. Strong brands that manage to create a reputation therefore simplify the decision making process and are welcome.
Of course, the greatest influencer for brand preference though is personal experience. If a company's products have served you well in the past, you are more likely to go with the same based on trust that they'll continue to serve you well.
Thus we have 'Brand Loyalty', which is part of the decision making process as a mental shortcut to let us get on with other things instead of being constantly immersed in researching products to buy. This will of course be a very personal thing. Some folk will research a lot, especially for big ticket items. Some will not care and buy on colour or style. Generally, people have some preferences for some products that aren't exhaustively researched but based on 'good enough' experience/data for the buyer.
This brings us to consoles and where consumers are going to go. some are arguing that it's price that matters and consumers aren't brand loyal. Well, consider the hypothetical case that PS5 releases at $500, and some unknown Chinese box built to the same quality as PS5 and its same spec for $250, the "Golden Rabbit Happy Joy Box." How well is that Chinese box going to sell? We all know it wouldn't go on to take the market by storm because it's untrusted. Hence we see that the reputation for PS is influencing buyers significantly.
PS is therefore way out in front for console brand - PS1 was great, PS2 was great, PS3 was okay, but thanks to the prior two generations, there was enough faith in the faithful to believe Sony could go back to form. Coupled with being cheaper and MS's snafu's, PS4 had a clear advantage. That now means 3 out of 4 top-draw brand-strengthening products. The mainstream gamer associates PS with mainstream gaming- how can they not? MS releasing a cheaper, similar product can't expect people to switch because of brand strength and shoppers preferring the product they know rather than taking a chance on an unknown. MS OTOH has struggled with a brand that muddles with their corporate brand. MS as a brand was not favourable when XB launched because Windows caused so many headaches. 360 saw a great product well marketed gain share because the rival screwed up so much, making it feel less risky to take a chance on a different brand. PS4's return to form coupled with XB1's disastrous start saw the XB identity weakened somewhat. So going into next gen, I think it's pretty apparent that people's psychology is going to favour picking PS5 over Scartlett as a default starting-place for the buying decision, and it's from there that different prices, services, etc. will have to swing people.
TL;DR If there is just one console next gen, sold by both companies at the same price with the same games, only one with a PS badge and one with an XB badge, the PS will sell better because consumers have already accepted PS and there's no reason to consider the other option, and this is what Brand Loyalty is - a general preference towards a product based on knowing who it's from and trusting, due to influences (prior experience, popularity, marketing), that its a good choice without having to go research the market for options.