The paper includes a caveat at the end: "Our study has several limitations. First, although the trial was formally double-blinded, assignment to placebo or LSD was unavoidably unblinded by the obvious psychedelic effects caused by the dose used."
They are similar but different. They both are a departure from being sober. I think in one study about ecstasy they used an amphetamine as the placebo, because both get you wired but in different ways.