Feature.fm supports three different options for publishing a Custom URL.
Root Domain (A Record)
In the example of a URL https://www.yoururl.com/album123, the root domain would be yoururl.com. Root Domains used for Feature.fm smart links cannot be used for any other site (e.g. your official website, merch store, etc).
While you would be creating new links off this domain on Feature.fm, your domain registrar (eg. Google Domains, Squarespace, Wordpress, etc.) is responsible for hosting and maintaining the DNS record.
Subdomain (CNAME)
In the example of a URL https://music.yoururl.com/album123, the subdomain would be music.yoururl.com. If you have a root domain (e.g. yoururl.com) that is used for hosting another online location - an official website, blog, or store - then creating a unique subdomain dedicated for creating Feature.fm smart links may be a good option for you.
While you would be creating new links off this subdomain on Feature.fm, your domain registrar (eg. Google Domains, Squarespace, Wordpress, etc.), would still be responsible for hosting and maintaining it.
Fully Managed
This option is only available on the Pro Marketer plan.
In the example of a URL https://www.yoururl.com/album123, yoururl.com would be what you submit for the Fully Managed option. You can create subdomains from within Feature.fm off of a fully managed domain (i.e. artist1.yoururl.com, artist2.yoururl.com, etc.) and individual smart links from both the primary domain and any assigned subdomains.
With the fully managed option, Feature.fm will be responsible for hosting and maintaining the DNS record.