With define
you register a module in require.js that you can then depend on in other module definitions or require statements.
With require
you “just” load/use a module or javascript file that can be loaded by require.js.
For examples have a look at the documentation
My rule of thumb:
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Define: If you want to declare a module other parts of your application will depend on.
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Require: If you just want to load and use stuff.