Is there a chance we can have different field label per page layout? For example... I have 2 account record types and i want a field in one record type to be BirthDate and in another date founded.
On one level, it's possible, and that's when dealing with translated labels based on user locale.
What you're proposing different. As a design choice, this pattern is understandable under some circumstances in other platforms where perhaps optimizing for storage is a goal.
However in the multi tenant custom object/field model, this kind of optimization doesn't really buy you any benefit. The "cost" of data storage for a record is identical, whether that record has 2 fields, or 200 fields.
In fact, the standard UI features of the platform are really designed around adding an extra field in precisely this type of circumstance.
You then use each field for each respective page layout.
In general, for Salesforce data model, I'd suggest you store data that is semantically different in different fields. Even if it is kind of similar, as is the case here.