1. CC6 Server is a bit vague... In a non-co-resident configuration, you need at least a CCMS (old term: SCCS), CCMA (old term: SWCP), CCSU (old term: SCCS fat client), and CCLM (new app for managing licenses)
As I recall, you must put the CCSU, CCLM and CCMS on your primary server. You would put CCMA on a separate server. This would be a fairly standard non-co-resident configuration. You can install CCSU on other servers, but there are some limitations, see the documentation for full details.
Presumably, you are asking just about the CCMS, CCLM and CCSU server... the CCMA server would be for administration only. You might do this if you were installing multiple CCMS servers at multiple sites and wanted to ensure that there was no local administration for each box so that you could administer web access on the single CCMA server.
2. CC6 Standby Server: This is a redundant CCMS server that replicates all data from the Active CC6 CCMS server. It is not a hot-standby server. In order to put the standby server in to operation, you must change IP addresses and computer name to whatever your active server is configured as. While the Active and Standby server are both running, the Standby server is copying all data from the Active server continuously.
3. Co-resident server: This is where you install CCMS, CCSU, CCLM and the administration component, CCMA, all on one server. For a single-site installation, this is pretty typical.