Generate private key from seed phrase python

I basically followed the instructions here How to generate mycelium addresses from the 12 words in python

So my code is similar:

from bip32utils import BIP32Key
from bip32utils import BIP32_HARDEN
from bip32utils import Base58
import os, bip39

strength_bits = 128
entropy = os.urandom[strength_bits // 8]
wallet_generator = bip39.Mnemonic['english']
mnemonic = wallet_generator.to_mnemonic[entropy]
assert wallet_generator.to_entropy[mnemonic] == entropy  # see, bijective!

# Or specify the mnemonic directly if you prefer:
mnemonic = 'aware report movie exile buyer drum poverty supreme gym oppose float elegant'
passphrase = 'test'

seed = bip39.Mnemonic.to_seed[mnemonic, passphrase=passphrase]
key = BIP32Key.fromEntropy[seed]
account_number = 0
i = 0
print "Address: " + key.ChildKey[44 + BIP32_HARDEN] \
         .ChildKey[0 + BIP32_HARDEN] \
         .ChildKey[account_number + BIP32_HARDEN] \
         .ChildKey[0] \
         .ChildKey[i] \
         .Address[]

And I verified it using //iancoleman.io/bip39/#english that the generated address is indeed the first address that this webpage generated as well. However, I also want to get the public and private key pairs using this same library. I originally tried:

print "Public Key: " + Base58.check_encode[key.ChildKey[44 + BIP32_HARDEN] \
         .ChildKey[0 + BIP32_HARDEN] \
         .ChildKey[account_number + BIP32_HARDEN] \
         .ChildKey[0] \
         .ChildKey[i] \
         .PublicKey[]]

print "Private Key: " + Base58.check_encode[key.ChildKey[44 + BIP32_HARDEN] \
         .ChildKey[0 + BIP32_HARDEN] \
         .ChildKey[account_number + BIP32_HARDEN] \
         .ChildKey[0] \
         .ChildKey[i] \
         .PrivateKey[]]

However, the output of these two calls are not the same as the ones provided by the website above for the same address.

So my question is: what's the proper way for me to generate the public and private key pairs?

Edit: To clarify, for the exact mnemonic and passphrase above, the website I'm using for reference tells me the first address and keypair should be:

While the output of the above python code is:

Address: 1K6WQtD7bLQ5nQ14GyBV33mBWSbkiRKhQs
Public Key: 62Yi9HBYYagf8CY1Ve2fquHKjBqAA7GFjGUUtkUHbkP5PHzv3W
Private Key: EGHMsAp7nY7Jo9F589zCU227KBLTDhiwRq5vYVvRVZxJNPJn4

So the address matches, but not the keypair.

>>> from bitcoinlib.wallets import Wallet
>>> mnemonic = "jaguar laptop random problem corn nut fun happy maximum federal wrap address"
>>> w = Wallet.create['Wallet1', keys=mnemonic, network='bitcoin']
>>> k = w.key_for_path[[0, 0]]
>>> k.address
'17AmSBNzGunnuPzCiJoTV2mdqu4v9Jt7QY'
>>> k = w.key_for_path[[0, 1]]
>>> k.address
'1Q9UgCADh26mfVaA5xmKxiCLZuiCG1g3zr'

Can you get private key from seed phrase?

Is private key the same as seed?

What is BIP39 seed?