Is there a tendency or custom or preference to use certain makes of grand pianos for certain types/styles of music? If so, what is the preference and what could be the reason?
Even though grand pianos do vary, the differences can't be compared to, for example, the obvious differences of electric vs. acoustic guitars and how they're used in genres. I'd go a bit back in the classification level and review things like the grand piano vs. upright piano vs. pianette vs. luthéal etc., to even attempt to say that one would be more suitable for certain genres than another. I think that the player's subjective opinion on the key touch and "playability" contributes to the choice of grand piano model the most. The recording space, microphone type/position and the recording engineer's choices also play a big role in how the grand piano will sound, and frankly, it's their job to make the sound fit the final mix, whatever other instruments are accompanying it.
There is a way to achieve different sounds within grand pianos, by the so-called preparations – objects which are placed onto the piano strings to alter the timbre and sound dynamics. These experimental sounds are excellent for cinematic music. For more, see the Wikipedia article on prepared pianos. You may also be interested in checking out a piano duo called Ferrante & Teicher, who were quite famous for their imaginative use of these modified grand pianos.
The way the piano has developed over the centuries is due both to 1) piano composers and performers influencing the piano makers' designs and inventions, and 2) to piano makers' new developments influencing how contemporaneous composers made innovations in their compositional techniques and demands on the performer. A great example of this is how Beethoven's compositions influenced the developments made by the Erard piano company. The range of the piano keys was increased because Beethoven's music demanded it. The piano was also strengthened in various ways because he wanted more power, he wanted the performer to be able to get a louder sound.
If you want to know more examples of this you should study the history of the pianoforte. From J.S. Bach's time to the present, the design of the piano has developed and changed in various (sometimes dramatic, sometimes subtle) ways. These historical, developmental changes have resulted in some (mostly subtle) differences in the characteristics of today's modern acoustic pianos. One example is the Bosendorfer. It is the only company that continues to make a piano that extends (the bass) beyond the conventional 88 keys.
Another, but much more complex design difference is found in the Bechstein. I don't know all the details, but the Bechstein company designed their piano to be exceptionally well-suited to Classical Era repertoire, especially Haydn and Mozart. The voicing of the registers is much more "transparent" which suits the way Haydn and Mozart composed their piano sonatas. There are of course some design changes or innovations that piano makers experimented with that didn't survive beyond their time.
To summarize, today's piano manufacturers each use a mostly-uniform yet subtly-unique design which results in each brand having particular strengths and weaknesses in relation to any particular "classical" style of music. (I'm speaking of Baroque, Classical, Romantic, Impressionistic, Expressionistic, etc. when I refer to "styles".)