How do design for SCDs in FM? Does a design for one SCD be different from the other
Yes. It is a highly detailed and specific issue. One answer does not apply to all. It depends on how your dimension changed. A general idea to make it work is to have Type2 or Type3 dimension so that you can have the earlier and the new hierarchy in place for a time range.
Read the parts of Kimball (Adamson's star schema is good too) about SCDs. Look at the sample models. The employee dimension in great outdoors warehouse is a type II. The employee dimension tables in great outdoors sales would be a good example of type III if the fact grain was at the employee history table level rather than employee (which is why it is filtered to the current record).
Closely related to the topic of how to model SCDs in FM is the topic of how a member is generated and identified and the concept of a member unique name (MUN).