First of all Dialog instance does not have its own database. So, it has to use database of CI. So while installing DI, you have to use SID of database of CI only.
Second as far as DB SID is concerned you can choose same SID as of SAP or different SID. There is no compulsion here. We generally choose DB SID same as of SA SID so that it can ease the administration.
If your DB SID and yor SAP SID are different that it is MCOD installation which is a different installation method when compared to the regular one where DB SID = SAP SID as said both method are feasible. It finally depends on your requirement to choose which method to rely on.
Sorry but ur explanation for MCOD is not the right one. MCOD is the process of installing Multiple Components on One Database.
Having SAP SID and DB SID different doesn't mean that u r installing MCOD.
Coming to the original query, as Sunny mentioned, it is not mandatory to have DB SID and the SAP SID as one and the same. We can have different SID for DB and SAP on a SAP installation. In case if u have a bigger landscape it is better to go with same SID to have better identification.
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