When I read a short story and my professor asks me to write about the general character and values of the speaker, is the character the one that wrote the story?
First, you must differentiate between narrator and speaker. If "speaker" simply means a character who says something in the story, then that character "wrote" the story (in a sense) only if he/she is also the first person narrator. This is usually the case. Think of Nick Carraway in The Great Gatsby.
This depends on the point of view. If the story is written in the third person, the narrator uses "he, she, they, etc." In other words, the narrator never uses "I" because he/she is not in the story. If this is the case, the third person narrator is not really a character in the story. You might be able to describe the values and characteristics of the narrator, as one removed from the world of the story. There is a sense that a third person narrator tells the reader the story and in that sense seems to have written it. But the third person narrator is not a character in the story.
If the story is written in the first person ("I"), it is more clear. In The Great Gatsby, Nick Carraway is the narrator and a character in the novel. He is the narrative speaker and he actually speaks to other characters in the novel. To be clear, Nick is not F. Scott Fitzgerald, but since Nick is the character telling us (narrating) the story, we can say that Nick is the one who wrote the story (within the context of the story itself). So, in a case like this, the speaker/narrator (Nick) is a character who "wrote" the story because it is he who relates it to us (readers).
It appears that what your teacher means by character is the other meaning of this word, as in, the personal virtue, values, and personality that this person has. Your teacher does not mean character in terms of a character in the story. I am unsure if there was any confusion there, but I wanted to be certain that was clear.
The previous answer makes a great distinction between the narrator and the speaker. The speaker can be a different character at different points in the story. It is simply whomever is speaking at the time. If you are reading outside of dialog, then the speaker and the narrator are the same person in that moment, if that makes sense.
It's tough without knowing the story you are discussing, but my guess is that your teacher wants you to read the tone of the story and say what sort of values, ethics, and key personality traits the person speaking has based on his/her tone, diction, and overall narration. The previous answer gets it right that the speaker is not necessarily the person narrating the story, and of course the speaker is not the author in a work of fiction. What do we learn about what this person's personal character is based on the way that he/she speaks? I hope this gives you some clarification.