While mixed-signal oscilloscopes can contain the functionality of a logic analyzer, such was not always the case and thus the need for differentiation between o-scopes and a logic analyzer. In this tutorial Bald Engineer gives a simple, easily explained walkthrough on some of the history, terms, and uses for a logic analyzer.
The basic idea behind a logic analyzer is to sample multiple inputs, or channels, of data at the same, recording each channel’s state as a single bit. For example, if you have an 8-bit logic analyzer, each “sample” it will take 1 byte of data across all eight channels.
If you are familiar with analog-to-digital converters, then you can think of a logic analyzer channel as a 1-bit ADC. It can only store one value: on or off.