but which of them really changes the timbre of their sound ?
The shortest answer would be - "all of them." It's one of the main reasons why there are so many different types of strings to begin with. The gauge, material, and winding affect the overall quality of the sound. Even coating on guitar strings changes the timbre and tone - even though strings are coated mainly for the purpose of preservation, the coating definitely changes the quality of sound... love it or hate it.
Some guitarists spend years experimenting with strings to find the right fit... generally, once a musician discovers their preferred string, they tend to play with it exclusively.
As far as the material of a string, for classical guitar in particular, this article is helpful in answering your question.
Clear Nylon: This is the most common material for treble nylon strings. Clear nylon offers a good balance of brightness and warmth in
tone and are known for their projection and sustain qualities and easy
vibrato.They aren’t as loud or as powerful as other string materials
like titanium or composite.
It is the smoothest material used for nylon strings, which can feel
the best when playing finger style.
Black Nylon: This produces a warmer, more mellow tone with more treble overtones than clear nylon. It is a popular choice for folk.
Titanium: Titanium produces a brighter crisper sound. Strings made with titanium are often used to brighten up a darker sounding guitar.
They also have good sustain and easy vibrato.
Carbon Fibre: Strings made using carbon produce a loud sound and tend to be longer lasting. They are characterized by a short sustain
and can go beyond bright to a more ‘thin’ or ‘harsh’ sound. These can
work well depending on the guitar.
If your guitar already has a bright sound, then carbon strings are
likely to sound too bright but they can be good for a darker sounding
Composite: This material produces a very bright sound with strong projection. Composite is often used for G strings to make for a
smoother transition in sound between the treble and bass strings.
Bronze: Bronze windings are typically composed of 80% copper and 20% zinc. This material is sometimes known as 80/20 bronze, brass or
gold. These strings produce a bright sound with good sustain.
Silver: Silver windings are typically made of copper with a silver coating. Silver coated windings help to produce a warmer tone.