Reports are completely pre-configured searches which you can export as a .pdf (or, in some cases, an Excel file). While you can filter your data based on which filters are pre-built into the report, you cannot add or remove fields or additional search criteria.
Reports can generate a lot of data without requiring a lot of extra work. Reports are especially useful for credit card reconciliation, large exports intended for external systems, or whenever you need data an easy-to-read format.
However, since Reports are limited to the reports that have already been created, sometimes you'll need, or prefer, a list instead.
Basic Lists are searches that are mostly pre-constructed by Blackbaud. With a basic list, you choose the topic, then choose from a preset group of display fields and filters. This gives you more display and options than a report, but lists cannot be exported to .pdf -- they can be exported to Excel.
The main disadvantage to a basic list is that you are limited to which display fields and filters already exist within the topic that you have chosen, and you cannot control which objects are inner joins or outer joins. If you need to gather more data, or change the options on your objects, you'll need an Advanced Lists.
Advanced Lists are searches that you build from the ground up, starting with selecting your objects, then your display fields, and finally your filters. This gives you complete control over what data you choose to display. Like basic lists, advanced lists can be exported to Excel.
The disadvantage to using an advanced list is that it can be daunting to build and to troubleshoot. The good news is, there are a large number of advanced list templates which have been built for you to customize and save. Using an advanced list template to start your list allows you to get the hang of building an advanced list without having to start completely from scratch.