The mapping of your Entities would be the same, but each DBMS has a configuration file with the connections strings, connection providers, etc ...
EX: Using Postgres:
<hibernate-configuration xmlns="urn:nhibernate-configuration-2.2">
<session-factory>
<property name="connection.provider">NHibernate.Connection.DriverConnectionProvider</property>
<property name="dialect">NHibernate.Dialect.PostgreSQLDialect</property>
<property name="connection.driver_class">NHibernate.Driver.NpgsqlDriver</property>
<property name="connection.connection_string">Server=localhost;database=northwind;User Id=postgres;password=123456</property>
</session-factory>
</hibernate-configuration>
In the code:
Configuration configuration = new Configuration();
configuration.Configure("conpgsql.config");