Always On Failover Clustering vs Always On Availability Groups
To start with there is nothing called as Always On or Always ON availability groups it is simply called as Availability groups.


  
  Always On Clustering and Always On Availability Groups are 2 separate concepts. Clustering is a HA solution and AG is a DR solution. Is the Always On Clustering same as Windows server clustering?
  


Yes you are correct. Always on clustering means you have created availability groups on database(s) which is part of failover cluster instance (FCI) and availability groups simply means two standalone nodes which are part of WSFC or not are configured to form AG, there is no FCI here.


  
  To create an Always On cluster - we have to launch the installer and choose the "New SQL server failover cluster installation", then on every new node we need to launch the installer and choose "Add Node"
  


That is basically creating an SQL Server failover cluster instance. Yes after you have created an FCI you can go ahead and add the databases residing on FCI to an AG. This is what you are calling as Always On cluster and this is what official MS doc calls it.

For point 3 please refer to above two quotes. Again note the difference between AG and AG residing on FCI.


  
  Assuming we have a fresh SQL instance (with no HA/DR) and are planning to configure only AG, then we first need to ensure that the "Failover clustering" windows feature is enabled on each participating node.
  


If you are planning to configure ONLY AG you do not need failover cluster instance. AG can be configured with 2 or more nodes which are part of WSFC or not (starting from SQL Server 2017 we have clusterless AG). Remember an FCI will always require some kind of shared storage, OTOH AG does not requires any kind of shared storage.


  
  In above scenario, "Failover clustering" windows feature is enabled so is clustering a pre-requisite for AG? Is the concept of clustering in Point 2 and Point 4 the same.
  


WSFC is prerequisite for AG but starting from SQL Server 2017 you can have AG without WSFC but that is not a real AG. WSFC is prerequisite for FCI though.

EDIT:


  If I wish to configure both HA/DR using Always On (AG) and Failover Clustering, then is best practice to follow Point 2 and then point 4 or the opposite way? Also, should we use both the virtual cluster name and Listener or either one if sufficient?


You need to first configure WSFC then install FCI like you mentioned in point 2 and point 4 then create database and then configure availability groups. Virtual cluster name is for FCI while Listener is for AG. You cannot configure cluster without virtual cluster name you have to have one, but you can have AG without listener. The only work of listener is to direct connections to primary replica which can be on any of the node.


  What is difference between "SQL server failover cluster installation" and windows clustering?


Windows server failover cluster(WSFC) is windows server feature on which whole "clustering" technology is based while FCI is at SQL Server level which leverages WSFC for failovers to provide AH to SQL Server instance.