You can have a persistent User Account or just a temporary Subscription for an email address.
In Mailman 3, signing up means you are creating a Mailman account (a user), which is typically done through the web interface. Subscribing refers to the act of joining a specific mailing list, which can sometimes be done anonymously (without an account).
Here are the key advantages of signing up for a Mailman account (rather than just subscribing):
Centralized Preference Management: The biggest benefit is having a single account to manage all your mailing list subscriptions. You can log in to one place to:
Change settings (like digest mode, non-delivery status, etc.) for multiple lists.
Easily subscribe to or unsubscribe from lists.
Persistent Identity: Your Mailman account (user) is tied to a primary email address, but you can associate multiple email addresses with a single account. This is helpful if you use different addresses (e.g., home and work) and want to manage them all under one profile.
Search list archives: You can search old discussion through the web interface if you have an account.
Primary Address Synchronization: If you subscribe to a list "via primary address" and then change your primary email address on your Mailman account, your subscription for that list can automatically update to the new address.
Easier Unsubscribing: When you are logged in with your account, unsubscribing from a list is usually a simple click on a button on your preferences page, without needing to confirm via email or remember commands.
If you just subscribe via the email interface or the anonymous web form, you are typically creating a subscription tied only to that specific email address.
You will usually need to use a password/token (often emailed to you) or reply to a confirmation email to modify your subscription settings or unsubscribe later.
You manage each list separately, requiring you to access different pages or send different email commands for each one.