The mnemonic words given to you by the portfolios are a representation of entropy. This entropy is then passed to the hash function PBKDF2 to generate a seed. The industry standard for this mnemonic-to-seed conversion is documented in BIP 39 and most portfolios follow this method. The seed is then passed to
HMAC-SHA512 to obtain a master extended private key.
Until then, implementations are standard and it is unlikely that you will encounter problems with different portfolio implementations. But after this step, the derivation becomes a little more complicated. There are a number of methods from there. You can use BIP 32, BIP 44, BIP 49, or BIP 84 derivation methods to generate individual private keys from the master private key. Then there will be a distinction between the hardened bypass and the unhardened shunt between different portfolios. Each bypass path will give you a set of keys that is completely different from other paths.
A spreadsheet here follows the diversion paths of many portfolios (please check the data yourself as they may be dated or incorrect). I've pasted the diversion paths of different portfolios below from the linked spreadsheet.
For example, when using a portfolio, you should note the diversion path followed by the portfolio for later retrieval. Also note that using a passphrase with the mnemonic words will generate a completely different set of keys compared to the exclusive use of mnemonic words.