Algorithmic Trading is trading using algorithms relevant to your trading style, whether you favour manual or automated trading. [This contrasts with the usual definition e.g. Wikipedia, however, I feel the mainstream definition is imprecise].
A trader should use all the tools available to them to maximise their profit. A key tool is technology. So a trader should use technology appropriate to their style of trading to get the most out of their trades.
Algorithms are simply programs, a type of technology. I define PUT THIS AT TOP?
However, all trading styles, ranging from fully Automatic to fully Manual, can benefit from algorithms and hence Algorithmic Trading. Below is a diagram to help clarify. I distinguish 4 types of traders by their usage of technology in the Analysis of setups and Execution of trades:
Fundamental Formula of Trading?
Frequency - Alerts
RR - Better execution
Win rate - Backtesting
This contrasts with how Algorithmic Trading is usually interpreted, i.e. "Automated" or "Black-Box" Trading, as per the definition in Wikipedia. LINK.