"When do you think that she will tell you about her difficulty?"
Translation:מתי אתה חושב שהיא תספר לךָ על הקושי שלה?
They are very close and most of the time can be used interchangeably. תגיד comes from the root ה.ג.ד, and תספר comes from ס.פ.ר. The former is about a statement = היגד (heyged) and the latter is about a story = סיפור (sipur).
(This is an explanation for advanced speakers who know the hebrew verb conjugation well). The root of תגיד is נ.ג.ד, not ה.ג.ד. It may seem a bit strange because there is no נ in the verb, but the origin of the verb is הנגיד, which becomes הגיד. The נ is dropped and the ג gets a dagesh (called דגש משלים). This verb is part of גזרת חפ"נ. (Another example of a verb in גזרת חפ"נ is הפיל - advanced speakers can easily see that its root is נפל because of its meaning.)
By the way, most native hebrew speakers also will think that the root is something like ה.ג.ד. Advanced verb conjugation is taught in high school, but most people don't remember it.