OPC “Classic” refers to a set of older OPC specifications that use Microsoft DCOM as their underlying communication mechanism. These are specifications such as OPC Data Access, OPC Alarms and Events, and others.
QuickOPC-Classic products (QuickOPC.NET and QuickOPC-COM) allow native connections to OPC “Classic” servers.
QuickOPC-UA is not a native OPC “Classic” client, but you can still use it to connect to OPC “Classic” servers, using so-called UA Wrapper (for OPC COM Servers) that is available from e.g. from the OPC Foundation (as part of OPC UA COM Interop Components). The OPC UA COM Interop Components from OPC Foundation make it possible for existing COM-based applications to communicate with UA applications.