All psychedelics are different by structure and for all chemicals, slight changes in the structure alter how they interact with the body.

DMT is very similar to tryptophan, an essential amino acid that the body uses. This slight modification makes it a drug which binds to a group of receptors in the brain that cause the hallucinations during the consumption. Due to certain enzymes humans possess, DMT is very quickly broken down from the active drug to an inactive form unless those enzymes are inhibited (with MAOIs).

LSD is derived from an alkaloid found in fungus (and very similar to the alkaloid LSA) which while has some similar structural aspects (you can actually find DMTs structure in LSD), these changes drastically affect the rate of metabolism and which receptors it binds to.

So essentially, different chemicals interact differently with the human body because their overall shape changes how effectively they bind to enzymes. For example, diacetylmorphine (aka: heroin) and morphine are nearly identical but the slight change in the structure of dia-morphine gives it much stronger potency by weight.

So differences of LSD vs DMT: LSD lasts longer, triggers enzymes in the brain differently (certain serotonin and dopamine receptors), and is able to be absorbed through the skin and orally.

I'm guessing the 'differences' in how psychedelics feel while under the influence of them probably come from their differences in triggering serotonin receptors in the brain along with other unrelated enzymes. For example, the 2c-x series of psychedelics seem to cause a lot more vasoconstriction than LSD, which is probably from reactions with enzymes that handle those functions.

Essentially each drug has a 'fingerprint' of what it triggers in the human body and when you alter that, it changes how the drug is felt. Sort of like two actors playing the same role. They may say all the same words but their performances will be markedly different.