Not true. Converting from BTC to ETH is a taxable event, for example.
What if I transfer from a Bitcoin wallet to another Bitcoin wallet?
The IRS has designed crypto as a property, so you are subject to paying capital gains (or claiming capital losses) whenever you sell, convert, pay or earn. Converting one crypto to another (or to USD) is a taxable event, while transferring BTC in one wallet to another wallet is not (since you keep the same property). Further details at https://www.coinbase.com/bitcoin-taxes#paytaxes.
If you sell a car for more than you bought it for, you do owe taxes on that. https://www.carvana.com/research/2020/03/what-to-know-about-....
It is not since it is a different private key...
Again, the understanding of "property" is evolving in this environment, and there are areas of regulatory uncertainty (such as synthetic assets from staking collateral in money markets). However, transferring from one wallet to another is pretty safe territory.