Combinar tres consultas SQL

Esto podría funcionar para usted.

SElECT COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId 
AND (imgWidth != $maxImageWidth AND imgHeight = $maxImageHeight
OR imgWidth = $maxImageWidth AND imgHeight != $maxImageHeight
OR imgWidth = $maxImageWidth AND imgHeight = $maxImageHeight);

También creo que esto es equivalente, aunque no estoy seguro.

SElECT COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId 
AND (imgWidth = $maxImageWidth OR imgHeight = $maxImageHeight);

Según la solicitud, aquí hay una sola consulta que devuelve 3 filas.

SELECT 'ALL EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth = $maxImageWidth AND imgHeight = $maxImageHeight
UNION ALL
SELECT 'WIDTH EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth = $maxImageWidth AND imgHeight != $maxImageHeight;
UNION ALL
SELECT 'HEIGHT EQUAL' AS COL1,COUNT(*) AS imgCount FROM (
    SELECT imgHeight, imgWidth, imgId AS primaryId FROM primary_images  
    UNION ALL 
    SELECT imgHeight, imgWidth, primaryId FROM secondary_images
) AS union_table
WHERE primaryId = $imgId AND imgWidth != $maxImageWidth AND imgHeight = $maxImageHeight;