A use case is finer-grained and more detailed than a scenario. A scenario describes some purpose for which a user might use your software and all of the features of the software that they would require to achieve that purpose. For example:
Generate monthly invoice batch
1. User imports data from spreadsheets describing completed work
2. System identifies inconsistencies in data (cross check between
client ref, order code, and expected job type)
3. If consistent, PDFs produced and an XML file for import into account
system
A use case breaks down a specific item from the scenario:
Generate PDF invoice
1. Collect all work items within one month occurring under the same
order code
2. Add them line-by-line to invoice template document
3. Allocate sequential invoice number
4. Fill in client details
5. Calculate totals
6. If invoice overflows space in template, split later items into
another invoice
7. Record invoice totals (will be used in xml export later)
8. Convert filled in template to a PDF file and store in the output
directory
Scenarios describe the software at a high level and give a rationale for each feature of the system existing. Use cases give a detailed account of what each feature does.