That API is only for SharePoint 2013+
The user management REST API linked in your question is specifically for SharePoint 2013, and presumably works in SharePoint 2016 as well. This is regardless of whether the SharePoint environment is on premises or in the cloud.
Office 365 is currently a subset of SharePoint 2013/2016 in terms features and functionality.
Note that SharePoint 2007 and 2010 will not have this API.
SharePoint users and Azure AD accounts are not synonymous
Consider that SharePoint and AD can exist independently of each other.
SharePoint does not need to use Azure Active Directory for authentication. It can use a traditional on-premises or cloud-hosted Active Directory, or theoretically (starting with version 2010) can use any claims-based authentication provider aside from Active Directory.
SharePoint 2007 and 2010 could also support simple forms based authentication as well as custom authentication providers, but as noted previously, neither of those versions of SharePoint expose the REST API in question.
AD = Authentication; SharePoint User = Authorization
Azure AD is a claim provider. A claim provider is used for authentication; when you log on to SharePoint, SharePoint relies on Active Directory to determine that you are who you say you are. A user's SharePoint account is used for authorization; the SharePoint account is granted access to content within SharePoint on a site by site basis.
Information in AD vs information in SharePoint
When using Azure AD for authentication, there are usually some areas of overlap between the data in SharePoint and the data in AD.
SharePoint's user profile service is usually set up to synchronize data from Active Directory to SharePoint, so that AD serves as the master data set for things like user display name and title. However, not all information is necessarily sync'd from AD to SharePoint, and additional information can be tacked on to SharePoint user profiles.
Group Membership in AD vs Group Membership in SharePoint
In Azure AD, a user can be a member of multiple groups. Groups can include both Active Directory groups (which can be nested) and Office 365 (SharePoint) groups (which cannot be nested).
A SharePoint user can only be a member of SharePoint groups, since SharePoint does not keep track of membership of Active Directory groups. That said, a user may have access to content in SharePoint indirectly due to an Active Directory group having been granted access.
AD User Scope vs SharePoint User Scope
Unless you're working directly with the user profile service, when you work with SharePoint users programmatically, they need to be retrieved from a specific site in SharePoint. This is because each site collection has its own set of groups which cannot be used on other site collections within the SharePoint farm, so group membership is tracked only on a site-by-site basis.
Note that this means that a user's lookup ID number (which is different from their login name) may vary between site collections. This also means that a user's collection of groups will vary depending on the site from which the user object was retrieved.
An Azure AD user has no such silos.