Teiid offers two separate connections for JDBC and Administration.
JDBC: With default port on 31000, is used to make JDBC connections to Teiid VDB to issue SQL queries. The URL format for this is "jdbc:teiid:vdb@mm://host:port"
Admin: With default port on 31443, is used to make admin connections that can be used to make administrative calls to Teiid Server. Like deploying a VDB, creating a data source or checking current sessions etc. For more information about all the supported admin calls check out "org.teiid.adminapi.Admin" class. The URL format for this is "mms://host:port". "mms" instead of "mm" for protocol because this is a secure connection using anonymous SSL by default.
I know that the above two URLs you provided in your post work currently in 7.2, however starting 7.3, they will not work. Only respective connections will be awarded on given ports.
There is some confusion introduced by Designer in creating these connections from Designer to Teiid server (it does not make explicit that which connection you are making), however these issues are now fixed and will be part of forth coming 7.2 Designer to be released very very soon (like this week).
Thanks for your clean answer.