Active Directory is Microsoft's LDAP[1] server offering. Eventually it got more features and is used by firms to enforce company wide (or group wide) rules like "Every computer must lock after 5min of inactivity" or "Adobe Acrobat must be installed in all computers".
Azure Active Directory is the cloud version of Active Diretory. It has some extra features compared to on prem AD (MFA, SSO with 3rd paty apps...) but the whole endpoint management part was moved to another product (Microsoft Endpoint Manager).
The reason so many companies have an AAD tenant is it is set up automatically when you configure Microsoft 365.
on-prem AD has SSO, it's called Active Directory Federation Services. Compared to Azure AD, the on-prem Federation Services has more features. To give one example, Azure AD does SAML, but it's not full compliant. We ran into an issue with at my last employer when a partner moved from AD-FS to Azure Active directory and broke the SAML integration. It required us to go back and re-do the federation model from scratch.
Azure Active Directory is the cloud version of Active Diretory. It has some extra features compared to on prem AD (MFA, SSO with 3rd paty apps...) but the whole endpoint management part was moved to another product (Microsoft Endpoint Manager).
The reason so many companies have an AAD tenant is it is set up automatically when you configure Microsoft 365.
[1] https://en.wikipedia.org/wiki/Lightweight_Directory_Access_P...