When you run below query, your are asking mysql to display the result of database() function. (Reference).

mysql> select database();

But in the below case, mysql throws an error as no database is selected till this point.

mysql> select databese();
ERROR 1046 (3D000): No database selected

When you have selected a database, mysql looks for a function named databese() within your DB but since it is not defined it throws the given error.

mysql> select databese();
ERROR 1305 (42000): FUNCTION hoge.databese does not exist