The way I hear my voice and how my voice sounds to other people are different.
The way my voice sounds to me and what it actually sounds like are not the same.
この場合、次のように言えると思います。
ーThe way I hear my voice and how my voice sounds to other people are different.
「自分に聞こえる自分の声と、人に聞こえる自分の声は異なる」
A and B are different という言い方。
ーThe way my voice sounds to me and what it actually sounds like are not the same.
「自分に聞こえる自分の声と、（自分の声が）実際にどのように聞こえるかは同じではない」
A and B are not the same. という言い方。
ご参考まで！
カナダ 
