Tutti & Solo notation
From the perspective of an amateur player: basson in amateur symphony orchestra.
As example, we recently played the Mozart A major Clarinetto Concerto. Here the music alternates between the solo clarinet and the orchestra. Every player has a carefully created part, my was bassoon 1 as there was a bassoon 2 as well. Only the director has a full score, showing all the instruments. You may look onto these parts on www.imslp.org.
In my part it says Solo in several places. This indiciets that the clarinet plays the main part. I then listen to the clarinet and support the phrasing and intonation of the solo part as best as I can. The clarinet is free to do tempo changes and play stronger or softer. The player may elect to interpret the written notes in order to create music. The purpose of the whole orchestra in these areas is to be a background to the solo, supporting. In my part, if I cannot hear the clarinet, I need to play softer. In effect the solo player leads the orchestra. If, not always, we have a director, he will follow the solist.
In some places it says Tutti. Here the orchestra plays the main part. The orchestra, including me, will play stronger. We, the orchestra, might add a bit more emotion, more vibrato, playing a bit more "look here". The leader of the orchestra will be the director or the first violin player, the concert master. I always try to position myself in order to see the concert master in order to be able to follow.
In a classical solo concerto, the lead changes between the soloist and the orchestra. In a symphony on the other hand, the lead changes between different instruments. If I find the notation solo in my part it will mean that I take the lead, this is "my" solo. It is very rare to see the notation tutti in a symphony.
In effect, the part I get is carefully prepared to help me play in the correct way.