Difference between a presidency city and …

Broadly, Presidency or Provinces were same thing, i.e. areas governed by British.However, Presidency was the seat of power from where Governor or Lt. Governor of British Company i.e. East India Company or British Govt. was residing and appointing his own staff for administration. When British came to India in 1604, they got some trading concessions from Mogul Emperor Jahangir and established their seat at Hoogly, afterwards they moved to Calcutta after defeating a weak Nawab Sirajuddola of Bengal in a flimsy fight by Lord Clive. Lord Clive begun ruling that area and it was under British protection. It was called Calcutta Presidency. Later on British expended to Madras Presidency, Bombay Presidency etc. On 1834 they made a legislative council and these Presidencies were properly established from administration, trading and expansion of Company Raj point of view.
Lateron the areas annexed or won after fight or treaty came under the concerned Presidency, was ruled by the Governor or Lt. Governor of that Presidency.
The said area ruled directly by British India Govwrnors called Provinces. Where he could direct recruit employees for the Government.