Display different record types as related list under an object

Record types are primarily used when you want to identify or "group" records that are used for a similar purpose or where its beneficial to identify them as being "related" or "similar".

Your question covers more than just record types. It also addresses how they can be utilized in terms of file sharing, restricting basic CRUD and impacting profiles. Your question interrelates all these issues.

Solution 1 assumes the need for two record types when perhaps there's only a need for one? Why do I say that? It appears to me that you primarily want to identify the records that either "belong" to or were "created by" Team A. Is that the case? After all, Team B can edit anything created or owned by Team A. So does Team B need their own record type? That's not totally clear yet.

As we know, there are often many ways of doing things in SF. I think there's an option that might suit your needs which you've not yet considered and that's Publisher Actions. You could have a Publisher Action that creates a new account based on the requirements needed for Team A and another Publisher Action based on the requirements needed for Team B. Both could use the same page layout, but only Team B Profile Users could also edit not only records created with the Team A Publisher Action, but also those created with the Team B Publisher Action. For those users with a Team A Profile, all fields they can't edit, would be read only unless you wanted them to have their own page layout appropriate for their profile.

Unless I'm mistaken, you could utilize record types for the above if you want to, or have new records default to the appropriate Publisher Action for the User Profile accessing the page. Whether to use record types really depends on whether or not there's a valid reason to segregate or "denote" a difference between records created by the two different teams and who has edit access to them.

I hope this answer is helpful to you. For more on this, I highly recommend you refer to Force.com Platform Fundamentals.

The record type drives the page layout. If you want to just have two record types, you cannot separate the layouts using the standard UI.

The alternative is a Visualforce page; this means you'd have to code four layouts, and use controller logic to determine how it should appear.

Personally, I'd go with the four record types. You could use a workflow rule to choose a record type in order to avoid the "label" of the record type giving too much information to the client.

Alternatively, you could hide the record type field entirely, and use a formula to display the record type to hide the distinction from your clients.