two SQL COUNT() queries?

In Sql Server or MySQL, you can do that with a CASE statement:

select 
    count(*) as TotalCount,
    sum(case when {conditions} then 1 else 0 end) as QualifiedCount
from MyTable

Edit: This also works if you use a JOIN in the condition:

select 
    count(*) as TotalCount,
    sum(case when {conditions} then 1 else 0 end) as QualifiedCount
from MyTable t
left join MyChair c on c.TableId = t.Id
group by t.id, t.[othercolums]

The GROUP BY is there to ensure you only find one row from the main table.

if you are just counting rows you could just use nested queries.

select 
    (SELECT COUNT(*) AS TotalCount FROM MyTable) as a,
    (SELECT COUNT(*) AS QualifiedCount FROM MyTable WHERE {conditions}) as b

One way is to join the table against itself:

select
   count(*) as TotalCount,
   count(s.id) as QualifiedCount
from
   MyTable a
left join
   MyTable s on s.id = a.id and {some conditions}

Another way is to use subqueries:

select
   (select count(*) from Mytable) as TotalCount,
   (select count(*) from Mytable where {some conditions}) as QualifiedCount

Or you can put the conditions in a case:

select
   count(*) as TotalCount,
   sum(case when {some conditions} then 1 else 0 end) as QualifiedCount
from
   MyTable

Related:

SQL Combining several SELECT results