CNN reports:
In 1995, the US Congress passed a law requiring America to move the embassy from Tel Aviv to Jerusalem. Proponents said the US should respect Israel's choice of Jerusalem as its capital, and recognize it as such.
The Jerusalem Embassy Act was the law passed by the United States Congress. Back to CNN:
Every President since 1995 -- Presidents Clinton, Bush and Obama -- has declined to move the embassy, citing national security interests. Every six months, the President has used the presidential waiver to circumvent the embassy move.
The Guardian reports:
Trump stressed that he was not stipulating how much of Jerusalem should be considered Israel’s capital. Palestinians see East Jerusalem as the capital of their own future state, and Trump did not rule out a future division of the city.
“We are not taking a position of any final status issues, including the specific boundaries of the Israeli sovereignty in Jerusalem, or the resolution of contested borders. Those questions are up to the parties involved,” the president said.
This conforms with the positions of previous administrations: that the final borders between Israel and Palestine in a potential two state solution are up to Israel and Palestine.
You ask
Or that East Jerusalem is Palestinian and West Jerusalem Israeli?
The Trump administration is neither saying this nor not saying this. This is exactly one of the issues that Israel and Palestine are supposed to resolve. It may be implicitly saying that West Jerusalem is Israeli, but it's not saying anything about East Jerusalem. Not saying is consistent with prior administrations.
It has been the official US position, since 1995, that West Jerusalem has been the Israeli capital and that the US was only delaying recognition of that fact until it was formally recognized by Palestine.
I don't know that any administration has taken a position on the legality of Israeli settlements in territory that is normally considered Palestinian. In general, the US position has been that the parties should agree on a resolution. As a result, the US has traditionally blocked the United Nations from condemning such settlements, even as the US has itself unofficially condemned the settlements. The Barack Obama administration broke that precedent when it allowed the UN to condemn Israel without exercising its Security Council veto. (CNN)