Inductive effect and hyperconjugation - one elephant, different parts?
Are the inductive effect and hyperconjugation both different ways of
  looking at the same phenomenon


I think so, both inductive and resonance (that's what hyperconjugation is after all) effects move electrons around.  I tend to separate the two effects as follows:


inductive effects are associated with electron movement through sigma bonds due to electronegativity differences
resonance effects are associated with electron movement through p orbitals due to electronegativity differences


For example, we often say that a methyl group stabilizes a double bond (carbon-carbon or carbonyl) or a carbocation.  The methyl group is roughly $\ce{sp^3}$ hybridized while the double bond carbon or carbocation carbon is roughly $\ce{sp^2}$ hybridized.  An $\ce{sp^2}$ orbital is generally lower in energy than an $\ce{sp^3}$ orbital because it contains more s-character.  Therefore electrons will generally prefer to flow from $\ce{sp^3}$ to $\ce{sp^2}$ orbitals.  The direction of this electron flow also indicates  that $\ce{sp^2}$ orbitals are more electronegative than $\ce{sp^3}$ orbitals.  How can the $\ce{sp^3}$ methyl group shift electrons to the lower energy, more electronegative $\ce{sp^2}$ carbon?  It can do it inductively (through sigma bonds) or through resonance (through p orbitals).

I've added a picture showing resonance structures involving hyperconjugation, just to be clear as to what hyperconjugation involves.