All sorts of terms are used for a voting district and it varies between countries too, so you can't place a firm meaning on these 2 words.
For example, in Britain, a constituency is an area that elects one MP to Parliament, and a ward is an area that elects councillors (usually 2 or 3) to the local council. But 'constituency' is often called ' a seat' instead. In Canada, each 'electorate' [ voting district] elects one member of parliament[ MP] to Parliament, but electoral districts are often known as "ridings" and the local group of a political party is called 'a riding association'. (Riding is an old English word for a part of a county.)