Vector bundles vs principal $G$-bundles

The difference is that, for a vector bundle, there is usually no natural Lie group action on the total space that acts transitively on the fibers. The fact that all of the fibers are, individually Lie groups, doesn't mean that there is a Lie group that acts on the whole space, restricting to each fiber to be a simply transitive action. The simplest example of this is the nontrivial line bundle over the circle. Another example is the tangent bundle of $S^2$.

I believe you have answered this yourself. Principal bundles are trivial iff they admit a global smooth section. Vector bundles always admit a global smooth section (zero section).

Therefore vector principal G-bundles are always trivial. The only available examples of vector G-bundles are thus of the form M x G, where G is both a vector space and a Lie group. Any examples of such G except for Abelian?

This is an old question, but I was just thinking about this question myself and I came to this realization:

For a vector bundle over a field $K$ of rank $n$, if it were a principal bundle, it would have to be a principal bundle for the additive group of the vector space $K^n$. However, as a vector bundle, the trivializations are glued along intersections via isomorphisms of vector spaces, ie elements of $\text{GL}_n(K)$, whereas for a principal $K^n$-bundle, the glueing is done by elements of $K^n$ (ie, translations). This means that not only is a vector bundle not a principal bundle, but also that a principal $K^n$ bundle is not a vector bundle.