The fundamental tension: trade fast and pay market-impact, or trade slowly and take timing risk. Every algo is a particular answer to that trade-off, and the right answer depends on your order size relative to volume and on how urgent your signal is.
The main families are schedule-based (twap-algorithm, vwap-algorithm), participation-based (pov-algorithm), and cost-based (arrival-price-benchmark). Liquidity-seeking variants add opportunistic taking when size appears.
For retail-sized orders in liquid instruments, none of this is needed; a limit order at the touch is fine. Algos start to matter when your order is a meaningful fraction of the book, which for a typical mid-cap might be a few thousand shares.
Related: twap-algorithm, vwap-algorithm, arrival-price-benchmark, market-impact