>>When you connect in SSMS, you have the option of connecting to either service (SQLEXPRESS or MSSQLSERVER). Actually, you should be able (in SSMS) to connect to SQLEXPRESS, and then to MSSQLSERVER, and you'll see both instances on the left side in Object explorer.
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>>When you connect to SSCM, it shows all the services on the box right away.
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>But why in SSMS I see my computer name in the field Server Name. If there is a server name the same as my computer name, shouldn't it be shown in SSCM?

I think SSCM is just generically showing it as "local".