How to get multiple counts with one SQL query?

You can use a CASE statement with an aggregate function. This is basically the same thing as a PIVOT function in some RDBMS:

SELECT distributor_id,    count(*) AS total,    sum(case when level = 'exec' then 1 else 0 end) AS ExecCount,    sum(case when level = 'personal' then 1 else 0 end) AS PersonalCountFROM yourtableGROUP BY distributor_id

One way which works for sure

SELECT a.distributor_id,    (SELECT COUNT(*) FROM myTable WHERE level='personal' and distributor_id = a.distributor_id) as PersonalCount,    (SELECT COUNT(*) FROM myTable WHERE level='exec' and distributor_id = a.distributor_id) as ExecCount,    (SELECT COUNT(*) FROM myTable WHERE distributor_id = a.distributor_id) as TotalCountFROM (SELECT DISTINCT distributor_id FROM myTable) a ;

EDIT:
See @KevinBalmforth's break down of performance for why you likely don't want to use this method and instead should opt for @Taryn♦'s answer. I'm leaving this so people can understand their options.

SELECT     distributor_id,     COUNT(*) AS TOTAL,     COUNT(IF(level='exec',1,null)),    COUNT(IF(level='personal',1,null))FROM sometable;

COUNT only counts non null values and the DECODE will return non null value 1 only if your condition is satisfied.