"Soul winning" is generally associated with that Christian subculture which regards the "flesh" as inferior and the "spirit" superior (pseudo-gnostics), and thus the work of preaching the gospel is directed at saving souls in anticipation of the rapture.
"Kingdom building" I view as a more fully orbed approach to preaching the gospel which see all of man, complete in body and soul, as being the object of Christ's salvation program, in both this world and the next.
And, by extension, the world becomes open to the positive effect of the gospel as well. "For God so loved the world ...". Kingdom builders can see the work of bringing the good news in activities such as holding political office, creating beautiful art, or even cleaning streets. "Soul winners" tend to view traditional "evangelists" as the only means to their end.
Kingdom builders are "soul winners" in the best sense, but that is not always the case with the first group. They often see Kingdom building" as akin to polishing brass on a sinking ship.
An interesting article on the subject is Gnosticism, the Soul-Only “Gospel,” and the End Times .
As a side question, if you don't believe that modern day Israel is related to the Israel mentioned in the Bible, do you believe that America does not need to support or help her?
The United States of America as a political entity should assist all her political allies, whether they be England, Germany, Israel, Japan, South Korea, etc. There is no reason to treat Israel as politically different from any other nation.
However, I believe the US already spends far too much money bailing out its political friends with foreign aid. I would not oppose an across the board cutback including Israel.