Inventory Solution and Inventory Pack for Servers are actually quite different. To show (but one) of the areas where they differ - consider Microsoft SQL Server.
Inventory Solution, as part of its capability, does a Software Inventory and reports that Machine X has Microsoft SQL Server Standard 2012 installed. That is all it is able to see.
Inventory Pack for Servers can (provided rights) also be run on Machine X to provide deeper details of the SQL presence such as which Databases, their dbo, size, avail space, path, Growth Mode & size. This augments the capabilities of Inventory Solution for many of the Server specific areas.
Other areas that Inventory Pack for Servers covers by default
Exchange Servers
MySQL/Oracle
Network Infrastructure (DHCP, DNS, RRAS)
Web & Application Servers
Inventory Pack for Servers is now only available as an entitlement under Server Management Suite (or by proxy IT Management Suite).
The rights to install Inventory Solution will be largely defined in the EULA of the product where the entitlement comes from.
If it is purchased/maintained as Inventory Solution - it can be installed on either Client or Server platforms
If it is an entitlment under Client Management Suite - it can ONLY be installed on Client platforms
If it is an entitlement under either Server Management or IT Management Suites - it can be installed on either Client or Server platforms.