user4399: I don't think I've ever heard these terms 'slow rapid' and 'fast rapid' outside chess960. Just now I tried looking up "slow rapid" "chess" "fast rapid" and "slow rapid" "fast rapid" and then almost everything there is chess960.
In the 2019 WFRCC, the following I believe applies for the semi-finals and finals besides just the quarter-finals:

Each match of the quarterfinals consisted of two “slow” rapid games (45 minutes for 40 moves plus 15 minutes for the rest, without increment), two “fast” rapid games (15 minutes plus 2 seconds increment) and 2 blitz games (3 minutes plus 2 seconds increment). The games were weighted differently: 3 points for each slow rapid game, 2 points for each fast rapid game and 1 point for each blitz game.

In the 2022 WFRCC, whatever 'slow rapid' means, FIDE categorises their 25min games as slow rapid, same as their 45min games but unlike their 15min games which are 'fast rapid'.

The time control is so-called 'slow rapid': Each game is 30 moves in 25 minutes, plus 5 minutes for the rest of the game after move 30, plus 5 seconds increment per move starting from move 31.

Question: How does FIDE define 'slow rapid' and 'fast rapid' ?
Note 1: Actually about the rapid WCC, I read just now:

In order to promote viewership, time controls were set at 15 minutes per player, rather than the pre-2012 standard of 25 minutes.


In chess, 25 is in the same category as 15
But in 960, 25 is in the same category as 45.

Note 2: If rapid is just 10-59 minutes, then I don't think slow rapid just means above the midpoint of 35 minutes since '25 minutes per player for the first 30 moves, after which each player will receive additional 5 minutes on the clock and an increment of 5 seconds per move starting from move 31' converts to 32.5 minutes and is considered slow rapid.

user18809: For regular chess, there's no official definition other than "Blitz", "Rapid" and "Classical". Distinctions inside each of these three categories would be a matter of opinion.

user7726: Quoting from the FIDE Handbook
Appendix A defines "Rapid Chess":

A.1    A ‘Rapid chess’ game is one where either all the moves must be
completed in a fixed time of more than 10 minutes but less than 60
minutes for each player; or the time allotted plus 60 times any
increment is of more than 10 minutes but less than 60 minutes for each
player.

Appendix B defines "Blitz:":

B.1
A ‘blitz’ game is one where all the moves must be completed in a fixed
time of 10 minutes or less for each player; or the allotted time plus
60 times any increment is 10 minutes or less.

No other form of game is referred to -  so all other time controls fall under the same heading. I think most people would call this "Classical" but note FIDE uses no such term. It also does not talk about "Slow rapid" or "Fast rapid". So the short answer to the question on the title is it doesn't. IMO the use of slow and fast in the quoted text are merely qualifiers to the term rapid, indicating at which end of the spectrum the time controls fall, rather than an official designation.

4399: <p>I don't think I've ever heard these terms 'slow rapid' and 'fast rapid' outside chess960. Just now I tried looking up &quot;slow rapid&quot; &quot;chess&quot; &quot;fast rapid&quot; and &quot;slow rapid&quot; &quot;fast rapid&quot; and then almost everything there is chess960.</p>
<p>In the <a href="https://en.wikipedia.org/wiki/FIDE_World_Fischer_Random_Chess_Championship_2019" rel="nofollow noreferrer">2019 WFRCC</a>, the following I believe applies for the semi-finals and finals besides just the quarter-finals:</p>
<blockquote>
<p>Each match of the quarterfinals consisted of two “slow” rapid games (45 minutes for 40 moves plus 15 minutes for the rest, without increment), two “fast” rapid games (15 minutes plus 2 seconds increment) and 2 blitz games (3 minutes plus 2 seconds increment). The games were weighted differently: 3 points for each slow rapid game, 2 points for each fast rapid game and 1 point for each blitz game.</p>
</blockquote>
<p>In the <a href="https://en.wikipedia.org/wiki/FIDE_World_Fischer_Random_Chess_Championship_2022" rel="nofollow noreferrer">2022 WFRCC</a>, whatever 'slow rapid' means, <a href="https://www.frchess.com/news/battle-lines-are-drawn-group-stage-ready-to-begin" rel="nofollow noreferrer">FIDE categorises their 25min games as slow rapid</a>, same as their 45min games but unlike their 15min games which are 'fast rapid'.</p>
<blockquote>
<p>The time control is so-called 'slow rapid': Each game is 30 moves in 25 minutes, plus 5 minutes for the rest of the game after move 30, plus 5 seconds increment per move starting from move 31.</p>
</blockquote>
<p><strong>Question</strong>: How does FIDE define 'slow rapid' and 'fast rapid' ?</p>
<p><strong>Note 1</strong>: Actually about the <a href="https://en.wikipedia.org/wiki/World_Rapid_Chess_Championship#World_Rapid_&amp;_Blitz_Chess_Championships_(since_2012)" rel="nofollow noreferrer">rapid WCC</a>, I read just now:</p>
<blockquote>
<p>In order to promote viewership, time controls were set at 15 minutes per player, rather than the pre-2012 standard of 25 minutes.</p>
</blockquote>
<ul>
<li>In chess, 25 is in the same category as 15</li>
<li>But in 960, 25 is in the same category as 45.</li>
</ul>
<p><strong>Note 2</strong>: If <a href="https://chess.stackexchange.com/questions/41486/if-classical-is-120-minutes-and-rapid-is-10-59-minutes-then-whats-60-119-minu">rapid is just 10-59 minutes</a>, then I don't think slow rapid just means above the midpoint of 35 minutes since '25 minutes per player for the first 30 moves, after which each player will receive additional 5 minutes on the clock and an increment of 5 seconds per move starting from move 31' converts to 32.5 minutes and is considered <a href="https://chess.stackexchange.com/questions/41479/time-control-conversion-when-it-comes-to-bonus-time-after-eg-40-moves">slow rapid</a>.</p>
 18809: <p>For regular chess, there's no official definition other than &quot;Blitz&quot;, &quot;Rapid&quot; and &quot;Classical&quot;. Distinctions inside each of these three categories would be a matter of opinion.</p>
 7726: <p>Quoting from the <a href="https://handbook.fide.com/chapter/E012018" rel="nofollow noreferrer">FIDE</a> Handbook</p>
<p>Appendix A defines &quot;Rapid Chess&quot;:</p>
<blockquote>
<p>A.1    A ‘Rapid chess’ game is one where either all the moves must be
completed in a fixed time of more than 10 minutes but less than 60
minutes for each player; or the time allotted plus 60 times any
increment is of more than 10 minutes but less than 60 minutes for each
player.</p>
</blockquote>
<p>Appendix B defines &quot;Blitz:&quot;:</p>
<blockquote>
<p>B.1</p>
<p>A ‘blitz’ game is one where all the moves must be completed in a fixed
time of 10 minutes or less for each player; or the allotted time plus
60 times any increment is 10 minutes or less.</p>
</blockquote>
<p>No other form of game is referred to -  so all other time controls fall under the same heading. I think most people would call this &quot;Classical&quot; but note FIDE uses no such term. It also does not talk about &quot;Slow rapid&quot; or &quot;Fast rapid&quot;. So the short answer to the question on the title is it doesn't. IMO the use of slow and fast in the quoted text are merely qualifiers to the term rapid, indicating at which end of the spectrum the time controls fall, rather than an official designation.</p>
