Changeability of one ABAP object (Program, Class, DDIC-Object.....and Customizing) is controlled by two transactions: SE06 and SCC4.
System Change Option in transaction SE06 provides granularity on what repository and cross-client customizing objects can be modified. This is more of a global setting (regardless of the client) and is only for client-independent objects. In here, Repository objects are further subdivided into different groups (software components and name spaces) so you can set only which group can be changed.
"Not modifiable" in "Global setting" in SE06 overrides all other setting in SE06 and SCC4. That means, nothing in this system is changeable except some customizing defined as current setting. On the contrary, with "modifiable" as global setting it's possible to fine set some parts of this system as "modifiable" some as "not modifiable".
Please pay attention to the fact that the Global Setting within the System Option Change (via transation SE06) opens or closes the entire system, regardless of what the Client(tranactio SCC4) setting is set to.
Please refer to note 44268 (SE06) and note 40672 (SCC4) regarding system/client change option configurations.