Microsoft Excel has far more uses.

Yeah, spreadsheets.

If you learn the more advanced features of Excel, you can manage it like a database.

It can even rival Access in that capacity.

Access is a better database tool.

You can make great reports in Excel, do data analysis, generate graphs and track customer entries. Lookup tables, pivot tables and Macros make Excel as powerful as many data analysis software packages.

Why use Excel to track customer data, when Access can do the same?

Not everyone has Microsoft Access, but you can always export Access data to Excel or
Excel to another file format.

What are the advantages of Excel, aside from Excels being a killer app for replacing an accountant’s ledger?

Excel has a short learning curve for the basic functions and a lot of wizards for the advanced ones.

Where is Access better?

Excel starts to fail when the size grows beyond a certain point. Access lets you run queries and maintain multiple tables of data.

And then there is database validations and referential integrity.

Access does have more constraints to prevent junk being put in fields. Whereas Excel won’t complain unless it expects a number and gets text, though the related calculations will error out when you literally try do divide by X.
What should I learn first?

Learn Excel first, because you can use it almost immediately in place of Quicken or for math homework. Learn Access later, especially if you’ll be working somewhere that uses it.

Isn’t Access a default database tool? After all, everyone has Windows.
For big databases, there are plenty of people who just go with Oracle or SQL, not even bothering with Microsoft Access. But all those databases export data or reports to Excel.

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