A few notes, mostly for myself.
This plugin is really useful for doing regular backups of your site. The backups seem to be done fairly quickly, and can be stored (for free) on an external service, such as Google Drive, Amazon S3, Dropbox, FTP, etc.
Updraft does have a premium plugin which can handle migrations, but it is rather expensive for the average user.
All-in-One WP Migrate
This is a great plugin specifically for migrating a site from one server to another. It’s REALLY simple. It even takes into account your database, database user name, password, etc. Ironically, this plugin charges for what Updraft does for free, while Updraft does for free what All-in-One WP Migrate does for free.
I typically download the backup to my computer, rather than paying the $99 for an external storage, then start up the new site (where I am going to migrate), then upload the backup there, and it’s done.
I recommend only using All-in-One WP Migrate for migration, and UpdraftPlus for regular backups.