The main difference between the two methods of signature injection is how the signature is inserted into the email.
Signatures injected by the modern add-in when "add signature when composing email" is selected are inserted in to the email as it is composed.
Emails sent in this manner are never routed through the Signature 365 servers. This mode also allows you to select alternative signatures if assigned to the user, and allows the user to change their default signature if allowed in the admin portal.
Signatures injected using the Classic Agent are created within the Outlook built-in Signatures function, and inserted by Outlook.
These emails are routed to the Signature 365 servers if you also have server-side signatures enabled but are detected as having a signature and are not altered.
Additional signatures are selected from the Outlook Signatures option.
Using the modern add-in in preview mode, the signature is not inserted when the email is composed.
It is not possible to select an alternative signature in this mode.
More information on client-side signatures can be found here: Client-side signatures.
If you do not have the modern add-in installed, or are using a device which does not support the modern add-in or classic agent, email sent will be routed to the Signature 365 servers for injection.
In this mode, only the default signature can be injected to the email. Additional information on the process can be found here: Server-side signatures.