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The point is that g(t)=t^2 creates g as a "symbolic function" (properly a callable symbolic expression), whereas t^2 is a symbolic expression.
sage: g
t |--> t^2
sage: g(t)
t^2
sage: g.is_callable()
True
sage: g(t).is_callable()
False
Differentiating a functin gets you a function, whereas differentiating a symbolic expression gets you a symbolic expression :
sage: g.diff(t)
t |--> 2*t
sage: g(t).diff(t)
2*t
HTH,
