They may be the same or different. Line management is technically the lowest level of management in a management hierarchy. The line manager has direct reports that are non-managers. Non-line managers have managers as their direct reports.
Functional management is where the organization is grouped into functional specialties (e.g. marketing, finance, engineering, etc.). The functional managers have a responsibility to define how their function is to be carried out and how the employees will be developed to meet those functions. Very often these responsibilities fall upon the line managers in those functional organizational units.