user54137: Can we please clarify if there is any difference (because apparently some technical documentation explicitly requests to include apostrophes) between a derivation from extended private key (xprv) or public key (xpub) of a child subkey, where m = root (xprv or xpub).
m/44/0/0/0 and  m/44'/0'/0'/0
What are the meaning of the apostrophes and how / when should they be applied? Do they change anything in a derivation path -- will the derived child subkey be different with or without them?

user74873: The apostrophes show whether or not that particular derivation is hardened. 
The difference been hardened and non-hardened keys is described in BIP32.
See the wiki for some further detail. https://bitcoin.org/en/glossary/hardened-extended-key

54137: <p>Can we please clarify if there is any difference (because apparently some technical documentation explicitly requests to include apostrophes) between a derivation from extended private key (xprv) or public key (xpub) of a child subkey, where m = root (xprv or xpub).</p>

<p><code>m/44/0/0/0</code> and  <code>m/44'/0'/0'/0</code></p>

<p>What are the meaning of the apostrophes and how / when should they be applied? Do they change anything in a derivation path -- will the derived child subkey be different with or without them?</p>
 74873: <p>The apostrophes show whether or not that particular derivation is hardened. </p>

<p>The difference been hardened and non-hardened keys is described in BIP32.</p>

<p>See the wiki for some further detail. <a href="https://bitcoin.org/en/glossary/hardened-extended-key" rel="nofollow noreferrer">https://bitcoin.org/en/glossary/hardened-extended-key</a></p>
