Is there any difference (e.g. in functionality or anything else) between an Apple Developer Account as Individual and an Apple Developer Account as Company/Organization, except the name in the developers name in the App Store?
1. User access
If you or your client has Organisation account, he can give access to various users (through their email address) without disclosing the credentials of the main account and those users can get access to developer.apple.com too. On the other hand, Individual account do not allow to add any users so one will have to give the main account credentials to developers in order to build an application(create certificates, profile, etc). One can add various users by assigning different roles listed here
Also, If you’re enrolled as an individual and add users in App Store Connect, users receive access only to your content in App Store Connect and are not considered part of your team in the Apple Developer Program.
2. Testers
Adding multiple internal testers is possible with organisation program but not with Individual one.
3. Store listing
With individual account, apps are listed with Developer's personal name while in Organisation, they are listed under organisation name. eg Company name LLC