Your gut feeling is reasonably close, but not precisely correct.
The Constitution sets the baseline rules for the powers of and interactions among the branches of the federal government, as well as the powers of and interactions between the state and federal governments.
With only one exception (the dilution of a state's representation in the Senate), the Constitution can be amended to basically anything. It can make anything legal and it can make anything illegal. It generally addresses fairly high-leval legal principles, but there's no reason that it couldn't be amended to include a 9,000-page law specifically addressing every conceivable aspect of the regulation of nuclear energy.
As it stands now and as it always has, the Constitution permits the federal government to write laws only with respect to certain topics. The states, meanwhile, retain authority to write laws on virtually any other topic.
There are a variety of legal and historical reasons why prohibition took the form of a constitutional amendment while drug laws are handled legislatively, but one important consideration is the scope of Congress's power to regulate "interstate commerce."
At the time of prohibition, it was not clear that Congress could regulate commercial activity that took place entirely within a single state. So if you grew all the ingredients for your whiskey in Kentucky, and you distilled those ingredients in Kentucky, and then you sold your whiskey in Kentucky exclusively to residents of Kentucky, it seemed that your conduct was outside the reach of Congress, and that any attempt to regulate it would be vulnerable to a constitutional challenge. The solution, therefore, was to amend the constitution and give that authority to Congress.
About a decade after prohibition ended, though, the Supreme Court decided that the power to regulate interstate commerce includes not just transactions that cross state lines, but also any conduct that “exerts a substantial economic effect on interstate commerce” Wickard v. Filburn, 317 U.S. 111, 125 (1942). This broadens the Commerce Clause authority to cover virtually any economic activity. So even if you buy marijuana seeds from your next door neighbor, plant them in your own back yard, grow them for strictly personal use in your own home, and never sell anything to anyone, the courts will hold that your conduct affects the interstate market for marijuana, and is therefore subject to federal regulation.
This standard substantially lowers the bar for Congress to act without a constitutional amendment, which is a big part of the reason there hasn't been an amendment to address narcotic use.