Use a case statement to check for the different types of nodes.
If the p_id is null, then it is a root.
If the id is in the list of p_id's (meaning they are another node's parent), then it is a inner node.
Otherwise, it is a leaf node.
SELECT id,
CASE
WHEN ISNULL(p_id) THEN 'Root'
WHEN id IN (
SELECT p_id
FROM Tree
) THEN 'Inner'
ELSE 'Leaf'
END AS type
FROM Tree
ORDER BY id;