user76567: BIP142 when encoding a segwit P2WPKH address is using a base58 address format (address p2xtZoXeX5X8BP8JfFhQK2nD3emtjch7UeFm in the example). 
I understand that BIP142 predates BIP173 but are P2WPKH and Bech32 synonyms now? Is there such a thing as Base58 P2WPKH address?

user5406: P2WPKH and bech32 are not quite synonymous.
Native segwit describes a type of output schema in which the scriptPubKey (the "locking script") is composed of a witness version and a witness program. P2WPKH is a native segwit v0 output type.
Bech32 refers to an encoding scheme and an address format to represent a recipient's scriptPubKey in out-of-band communication.
We use "bech32 addresses" to instruct spenders to create "P2WPKH outputs":

Pay to Witness Public Key Hash (P2WPKH) and Pay to Witness Script Hash (P2WSH) are native segwit v0 outputs that get represented using bech32 addresses.
Pay to Public Key Hash (P2PKH) and Pay to Script Hash (P2SH) use base58 addresses.
Pay to Taproot (P2TR) and future native segwit output types will use bech32m addresses.


user48884: 
are P2WPKH and Bech32 synonyms now?

No. Bech32 is also used for P2WSH addresses. Native segwit and Bech32 are synonyms.

Is there such a thing as Base58 P2WPKH address?

No.

76567: <p><a href="https://github.com/bitcoin/bips/blob/master/bip-0142.mediawiki#example" rel="nofollow noreferrer">BIP142</a> when encoding a segwit P2WPKH address is using a base58 address format (address <code>p2xtZoXeX5X8BP8JfFhQK2nD3emtjch7UeFm</code> in the example). </p>

<p>I understand that BIP142 predates <a href="https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki" rel="nofollow noreferrer">BIP173</a> but are P2WPKH and Bech32 synonyms now? Is there such a thing as Base58 P2WPKH address?</p>
 5406: <p><em>P2WPKH</em> and <em>bech32</em> are not quite synonymous.</p>
<p><strong>Native segwit</strong> describes a type of output schema in which the <code>scriptPubKey</code> (the &quot;locking script&quot;) is composed of a witness version and a witness program. P2WPKH is a native segwit v0 output type.</p>
<p><strong>Bech32</strong> refers to an encoding scheme and an address format to represent a recipient's <code>scriptPubKey</code> in out-of-band communication.</p>
<p>We use &quot;bech32 addresses&quot; to instruct spenders to create &quot;P2WPKH outputs&quot;:</p>
<ul>
<li>Pay to Witness Public Key Hash (P2WPKH) and Pay to Witness Script Hash (P2WSH) are native segwit v0 outputs that get represented using <strong>bech32</strong> addresses.</li>
<li>Pay to Public Key Hash (P2PKH) and Pay to Script Hash (P2SH) use <strong>base58</strong> addresses.</li>
<li>Pay to Taproot (P2TR) and future native segwit output types will use <strong>bech32m</strong> addresses.</li>
</ul>
 48884: <blockquote>
  <p>are P2WPKH and Bech32 synonyms now?</p>
</blockquote>

<p>No. Bech32 is also used for P2WSH addresses. Native segwit and Bech32 are synonyms.</p>

<blockquote>
  <p>Is there such a thing as Base58 P2WPKH address?</p>
</blockquote>

<p>No.</p>
