You're probably already aware that most people's speaking voice covers a fairly small pitch range, usually near the lower end of what they can sing. (although it does vary)

The "singing voice," even in the same pitch range, likely will sound a little different, especially if the coach is trying to teach you to "open up" to get a little more resonance with your singing. Some voice teachers prefer to "teach" toward the upper end, at least at first, because for most people the sound naturally tends to be a little "thinner" there, so the effect of getting "full throat and lung resonance" is easier for the student to learn.

With practice, you likely will be more comfortable with what you hear in your singing. There also is the hazard that once you become more accustomed to "full voice" singing, you may find your speaking voice tends more to resemble what you've learned to sing - which is usually okay unless you get to where ordinary conversations sound like an oratorio.

John