I'm no expert but I'll try to outline some pharmacological reasons why ephedrine and amphetamine work differently. Biscuit has described well the chemical / structural differences.
From a chemical level it has to do with SAR, or structural activity relationships; the way the drug fits into or binds with your body molecules (receptors enzymes etc).
Receptors are large proteins, some of which are serpentine shaped(G protein) and others that are pockets which form small holes in the center that can be closed or opened (ion channels) to pass certain shaped molecules. There are others but these two are relevant here. These receptors are often located in the outer membranes of cells. They act as switches for certain cell functions, and gates into/ out of the cell for certain molecules.
There are other considerations, but these are some of the major factors affecting whether a molecule (ligand) such as amphetamine will bind with a certain receptor.
Whether the receptor is “available”
Shape of the ligand and how much it can easily twist or bend (rotational conformity)
Competition with other molecules
The size of the functional groups or atoms attached (-OH, H etc)
And the polarity of the atoms /groups attached
One thing to note, is while a ligand may be complex or simple, receptors are very complex molecules
Most binding between ligand and receptor is through hydrogen bonding, and other very weak electrostatic bonds (van der waals forces). Small electronic charges attract, repel or make still, atoms of the ligand - receptor which come very close together. Although the receptor can often change its shape considerably, it is highly selective about what it binds with. However it can still mean many different molecules can bind with a single receptor type.
Once it binds, a G protein receptor can completely rearrange itself, where it causes further chemical changes.
As Biscuit mentions Ephedrine has an alpha–OH. Oxygen is a very electronegative element, and very much bigger than H. Because of the angle the H is at when bound to O, it does not sit where the H or methyl group H’s would sit. Therefore the molecule may not bind at all in the place “amphetamine without the OH” would bind.
Sometimes these changes in atoms and functional groups (the H -->OH in this case) can still enable the molecule to bind, but alters its effect. This may produce more or less of the original effect, or cause a completely different effect. Different acting drugs and generics are often designed by such substitutions.
Ephedrine and Amphetamine (monoamines) both bind to some of the same receptors, such as some adrenoreceptors, but their actions here are quite weak. They work their magic by binding to the regulating receptors called uptake 1 receptors, which allows them to enter the noradrenaline (NA) producing (presynaptic) cell. As they enter they are bound up in things called vesticles (little bundles of proteins). Binding causes NA to be released in to cytosol (fluid inside cells). Some NA is broken down inside the cell by MAO (an enzyme called mono amine oxidase) but some escapes in exchange for the monoamine. This NA is now out side the cell ready to do its job
As well as binding with other receptors amphetamine also alters the regulatory mechanism for NA; as said it restricts uptake. More is circulating outside cells and enters the blood stream, where it is able to bind with other cells receptors.
Amphetamine also inhibits MAO which further increases its effects (more DA). Through both the actions on producing NA and other indirect actions on Dopamine (DA) receptors, Amphetamine also causes DA to be released in higher levels than normal, with the regulating mechanism for DA also turned towards off.
Dopamine as Biscuit says is what gives you the pleasure, elevated noradrenaline levels can be associated with amongst other things anxiety.
As BT mentions Ephedrine binds as an agonist (stimulates –turns on) with Beta adrenoreceptors, this probably being a lot to do with the shakes described, as tremor is the result of stimulating Beta 2 adrenoreceptors in skeletal muscle cells.
Long term ephedrine /pseudo use is known to cause receding of the gums. I knew some truck drivers years ago who used ephedrine virtually every day. 5 of the 6 in that crew all had receding gums and terrible teeth at ~30-35. Personally, although it has its uses in medicine, I think its of little value as a drug of pleasure.
This is far from a complete picture, many other mechanisms are at play, but hopefully it helps in some way with understanding why they work differently. Please correct anything anyone.