With respect to the concept of profit center and segment, both are the characteristics/scenarios which are assigned to the leading and non leading ledgers into the system to facilitate the organization for the preparation of financial statements on the basis of profit center or segment wise.
1) A profit center is an organizational unit below company code level in sap that reflects a management oriented structure of the organization for the purpose of internal controls generally used for preparing reports and financial statements which are internal required by management for assessment of profitability of the organisation example would be an organization having presence in India (India would be company code and the branches in India would be profit center's management would use profit center approach to calculate the profitability of each branch).
Related: PFCG Roles and Authorization Concept
2) As per IFRS sgements are nothing but the products or the different business of the organization according to which the financial statements for external and internal purpose are to be prepared, as per IFRS it is a necessity for each organization to define and prepare the financial statements segment wise (example would be a software company with different business consulting, software, training etc).