Is there a difference in function or behaviour between Clear Akonadi Cache in akonadiconsole and the same-named function in KMail?

I’m referring to KMail → Folder → Clear Akonadi Cache and Akonadi Console → Browser → (choose a folder) → right-click → Clear Akonadi Cache

Are they the same?

Yep, they call the same thing. The only difference I’m aware of is KMail offers to restart Akonadi for you, whereas with Akonadi Console, I assume it’s expected you’ll restart it manually.