Apple offers several excellent ways to migrate an existing Macintosh over to a new Mac.
The method that takes the least time is to use Target Disk Mode (Share Disk on Apple Silicon Macs) with the Migration Assistant to load up the new Mac.
Apple’s suggested method uses the Migration Assistant software on both computers, and does the transfer using Wi-Fi. A step by step set of instructions is available from Apple here ->
When a Time Machine copy of the old Mac exists, then the Migration Assistant can make use of a Time Machine backup.
Target Disk Mode
Target Disk Mode allows a Macintosh to be treated like an external disk by another Mac using the built in Thunderbolt (USB-C or Firewire) connections for maximum speed of transfer.
Steps
On the old Mac, restart the Mac, and hold down the T key. When the Mac has booted into Target Disk Mode, a disk icon will appear screen of the old Mac.
Connect the Thunderbolt port on the old Mac, to the new Mac. This may involve using a Thunderbolt to USB-C adaptor.
Start up the new Mac.
If this is the first time the Mac has been booted it will go through a startup process and gather basic information. When it reaches the screen with the Migration Assistant, select the option “From a Mac, Time Machine backup or Startup disk” and select the old Mac as the disk.
If the Mac has already launched, then open Migration Assistant from the Applications>Utilities folder and select the From a Mac, Time Machine backup or Startup disk” option and choose the old Mac as the disk.
In Migration assistant choose the information to transfer (usually all the users and data) and click Continue.
The transfer could take several hours to complete.
When done, the new Mac should have all the software, data and settings (including passwords) from the old Mac.