In India my understanding is that one has to take exchange permission for algorithms (to do algorithmic trading). So there must be some clear legal definition for algorithmic trading. Since many brokers provide APIs for very low cost any body can opt for programmatic access to markets instead of UI based access. So I will give some of situations. Let me know which one requires permission.
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Trader identifies multiple stocks to enter overnight and for ease of execution and speed uses API to place order in the morning. (Same scenario for exit also)
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Trader makes manual entry and writes a code for automated ATR based trailing stoploss exit using APIs
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Trader identifies stocks using some program and entry and exit is strictly manual (This is very common but just for sake of understanding)
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Trader identifies stocks using third party software (Or self written program). But uses API access for entry and exit.