Algorithm
An algorithm is a precise, unambiguous sequence of mathematical and computational rules designed to process input data, perform calculations and solve a specific problem. In artificial intelligence, algorithms analyse patterns in historical data and adjust a model's internal parameters, so the model learns underlying relationships and makes predictions without anyone writing explicit step-by-step instructions for each case.
In practice
The distinction that matters in a buying conversation is between a rules engine, where a person wrote the logic and can show it to you, and a learned model, where the logic was derived from data and cannot be read directly. The second is harder to audit and quietly degrades when the data it sees stops resembling the data it learned from.