Esplanade and promenade are sometimes used interchangeably, but that is a mistake. A promenade can be anywhere, and it is exclusively for walking, while an esplanade is for walking but also can include large boulevards or avenues with cars.
A Promenade, often abbreviated to '(The) Prom', was an area where people - couples and families especially - would go to walk for a while in order to 'be seen' and be considered part of 'society'.
In Southport, the Esplanade runs from Birkdale beach access to the Kingsway, and then becomes the Promenade up to the end of the Marine Lake. No difference between them. Then again, that's Southport for you.