Versioning is for editing in a multi-user environment. Replication is for replicating your data in a multi-database environment. They are two very different things.
In a multi-user environment the versioning is used to enable handling of conflicts where two (or more) editors may have edited the same feature. It gives the abililty to choose the correct edit when pushing those changes back to the default live version - what everyone else sees. Versions are not a copy of the data, rather the database keeps track of edits (creation, edit, deletion) and when these edits are posted, they are reconciled and updated in the default live version.
Replication is used to copy your data out to other databases - these may be in other locations, or just on the other side of a firewall. If users need to edit features in a replica then usually versioning is used to handle those edits, particularly as edits may also be coming in from other locations.
In our office we use both replication and versioning. Versioning because we have 10-20 users in the organisation that edit features across hundreds of feature classes. Replication because we push all our data through to a cloud server environment which is then made available on the web or in apps over the internet. Some editing also takes place via these apps, and are replicated back to our internal server environment.
Both versioning and replication require ArcGIS Standard or Advanced licenses.