In Python 2.7,

my = "my"
key = "key"
print(hashlib.sha256(my + key).hexdigest())
print(hmac.new(my, key, hashlib.sha256).hexdigest())

output,

5e50f405ace6cbdf17379f4b9f2b0c9f4144c5e380ea0b9298cb02ebd8ffe511
15a55993a27e0de7a4c4daa67a7c219199a464ca283797f545b783cce07b38a5

or have I misunderstood?

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