It does sound like they are using/recommending Always On...
This became available in SQL Server 2012 and is a combination of clustering and mirroring in SQL Server. Although you can setup what is called a BAG in Standard Edition - there are significant limitations. The goal of AlwaysOn is HA/DR - with the advantage of also being able to setup read-only secondaries. The main difference between AlwaysOn and traditional clustering is shared storage - AlwaysOn does not utilize shared storage - each system has its own dedicated storage (which means the DR node can be in another location - as long as the cluster can be created at the Windows level).
For your purposes - you will need Enterprise Edition licenses for the read-only secondary. But - you can also have multiple non-read only secondaries for HA/DR without additional licenses. Those secondaries would be setup/configured so you could fail over with minimal data loss.
You also cannot utilize SQL Server 2016 for the reporting system. It must be the same Edition and version of SQL Server - so your reporting system will be SQL Server 2014 (at the same SP and CU level).
To reduce costs - you do not have to have the same server configuration for the read-only secondary. It can have reduced number of CPUs and memory - but you do need enough to support the processing of transactions across the mirroring session. This will require more space in tempdb and you want those disks to be as fast as possible - since tempdb is heavily used for the version store.