Use of the term evolution in that context, but it's not terribly inaccurate.
If you accept that part of the evolution of a star is the process of accreting enough material to reach the minimal stellar mass, then it's accurate to say that a brown dwarf got farther along that path than a planet before it stopped. And yes "evolution" is the correct term in this context.
'Failed star' As if it tried, but just couldn't pull it off.
Exactly right. It accreted mass from a cloud of gas and dust and got pretty big, but just couldn't collect enough for whatever reason to sustain fusion and become a star. A "failed star". It's poetic, but accurate. Even Jupiter is sometimes described this way.
A decent article shouldn't call something a Brown Dwarf star and define it to be a 'star' which failed to achieve fusion. If it failed to achieve fusion, then it isn't a star, but ... a planet ;)
They don't call it a "Brown Dwarf star", they call it a Brown Dwarf, because "Brown Dwarf star" is not a thing since Brown Dwarfs are by definition sub-stellar objects. They may undergo some fusion, but not sustained fusion and so will steadily cool over their lifetime, unlike a star. Other differences are that a brown dwarf will be fully convective with no chemical differentiation by depth, unlike a star.
The line between brown dwarf and planet is fuzzy, and not dependent on the presence or absence of fusion at any point. Very large gas giants -- perhaps even Jupiter -- could have had some fusion occur.
So the correct nitpick would be that they didn't say "sustained fusion", implying that fusion never occurred.
A brown dwarf which isn't fusing anymore isn't a 'failed to become a star' star, but a star which has ceased fusion.
No, a brown dwarf which isn't fusing anymore is a brown dwarf, which is a "failed to become a star".
Not hot enough to be a white dwarf, and cooling to become a black dwarf.
A white dwarf is not a really hot brown dwarf and a black dwarf is not a really cool brown dwarf. A white dwarf is the remnant of a Main Sequence star that wasn't big enough to form a neutron star after its fusion-burning life is over. It's electron-degenerate matter. A black dwarf is a what white dwarfs will eventually become in something like 10^15 years when they finish cooling.
A White dwarf or black dwarfs is a has-been.
A Brown dwarfs is a never-was.
