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To answer your question about where to read about the difference, the live documentation might help. Compare the output from these:

sage: a = 10
sage: a.mod?
Signature:      a.mod(self, I)
Docstring:     
Return a representative for "self" modulo the ideal I (or the ideal
generated by the elements of I if I is not an ideal.)
... (and then some examples are provided)

vs.

sage: mod?
Signature:      mod(n, m, parent=None)
Call signature: mod(*args, **kwds)
Type:           cython_function_or_method
String form:    <cyfunction Mod at 0x10a31ca00>
File:           ~/Sage/git/sage/src/sage/rings/finite_rings/integer_mod.pyx
Docstring:     
Return the equivalence class of n modulo m as an element of \ZZ/m\ZZ.
...