Same query hash for totally different queries

While hash collisions are possible, I suspect what's happening is you're pulling the text for the whole batch, not the particular statement. A procedure with multiple statements can get a cache entry for each statement. And if some statements are identical across procedures, they'll have the same query hash. Let me demonstrate:

USE TestDB
GO

--DROP TABLE dbo.employees
CREATE TABLE dbo.employees (
ID INT IDENTITY PRIMARY KEY,
title VARCHAR(20),
salary TINYINT,
has_been_fired_yet BIT)

INSERT dbo.employees
VALUES ('Senior DBA',30,0),('Grumpy DBA',50,0)
GO

CREATE OR ALTER PROC dbo.Payroll
AS

SELECT 'Your total payroll is '+CONVERT(VARCHAR(10),SUM(salary))+' query bucks'
FROM dbo.employees
WHERE has_been_fired_yet = 0
GO

CREATE OR ALTER PROC dbo.RightSizing
AS

UPDATE dbo.employees
SET has_been_fired_yet = 1
WHERE salary > 40

SELECT 'Your total payroll is '+CONVERT(VARCHAR(10),SUM(salary))+' query bucks'
FROM dbo.employees
WHERE has_been_fired_yet = 0
GO

--EXEC to get them in the cache
EXEC dbo.Payroll
EXEC dbo.RightSizing

Use the below query to see the how the same statement that is in each proc shows up separately.

SELECT
st.text AS batch_text,
SUBSTRING(st.text, (qs.statement_start_offset/2) + 1,  
    ((CASE statement_end_offset   
        WHEN -1 THEN DATALENGTH(st.text)  
        ELSE qs.statement_end_offset 
    END - qs.statement_start_offset)/2) + 1
) AS statement_text,
qs.execution_count,
qs.query_hash
FROM sys.dm_exec_query_stats AS qs  
CROSS APPLY sys.dm_exec_sql_text(qs.sql_handle) as st 
WHERE st.objectid IN (OBJECT_ID('dbo.Payroll'),OBJECT_ID('dbo.RightSizing'))

If you use the query in your question, it fails to pick up the identical statement, since it looks at only the batch text.