select st.name,count(si.id)
      from  t_school_type st  
 left join  t_school_info si on st.id = si.t_s_id
     where si.record_status = 1
  group by st.name;

select st.name,count(si.id)
from  t_school_type st 
left join  (select * from t_school_info where record_status = 1)si on st.id = si.t_s_id
group by st.name;

------解决方案--------------------
    select st.name,count(si.id)
     from  t_school_type st 
  left join  t_school_info si on st.id = si.t_s_id
    where si.record_status = 1
 group by st.name;
------------------------------
the result will be
STEP 1:
select * from t_school_type st left join t_school_info si on st.id = si.t_s_id;
this sql will find out every entry in table t_school_type;
we can name the result as "resulttable"

but after you add where condition
STEP 2:
select name,count(id) from resulttable where record_status=1 group by name;
the result will be filted.

So that's why you got the result like that, it's true.