Undertand the syntaxe difference

 I want to know what is the difference in executing the queryselect * from tb_test where date_inc > to_date('31/10/2013','dd/mm/yyyy') that is not using the index created, and the query

select * from tb_test where date_inc between to_date('31/10/2013','dd/mm/yyyy') and trunc(sysdate+1) that is using the index and both queries returns the same records?