Proper way to export database to other servers
If you want the schema and the data, the best and safest way is a copy_only backup. Don't like the backup history that comes along in the MSDB tables? Ok, delete it, then start a new backup chain by performing a full backup once the copy is restored on the new server.

If you just want schema, there are plenty of options. I prefer RedGate's SQL Compare, but there are plenty of alternative tools, including SSDT which (I think with the most recent update) has schema compare functionality.