Hi Elliot Alderson,
Thanks for your post.
Based on my research, They are two different settings. The updatepassword is set in ADFS. By default, this functionality is disabled in ADFS. Change password looks just like another endpoint in ADFS and all you need to do is enable the endpoint.
And Self-service password reset is in Azure AD,
https://msdn.microsoft.com/en-us/library/azure/Dn683881.aspx
In addition, here are links for ADFS and Azure AD forums below, I suggest you also post for more support.
https://social.msdn.microsoft.com/Forums/vstudio/en-US/home?forum=Geneva
https://social.msdn.microsoft.com/Forums/en-US/home?forum=WindowsAzureAD
Best Regards,
Mary Dong