SQL Server domain account login and user
Unless you're referring to contained databases (which are new in SQL Server 2012), you can't use the second approach. Whenever a person authenticates to SQL Server, they are authenticating against a particular server login (or possibly multiple logins if you're creating logins for domain groups). This server login can then be mapped to one or more database users to allow access to different databases.

Unless you're doing some tricks with EXECUTE AS or using application roles, there's no way for somebody to authenticate directly as a database user without a server login being mapped to it.