You enlarge / {shrink} yourself as if you had cast Enlarge Reduce on yourself.
It's a statement linked to a particular spell1
I think that you are over-complicating this semantic / usage difference.
The only two "as if you had" statements have to do with the same spell's effect (Enlarge Reduce, 2d level, transmutation) which make the magical effect to either shrink or enlarge (caster's choice) a target. The wand casts the spell (not the caster) thus "wand casts it as if you had" to create the magical effect.
But wait, the wand always chooses! Roll d100 for results
For this particular spell, when the caster chooses themselves the caster won't get a saving throw since a saving throw is for an unwilling creature.
If the target is unwilling, it can make a Constitution saving throw1.
(I can see different DM's choosing to rule differently on that due to the overarching "spell save DC 15 versus effects" ... but more below).
- Compare this to the 98-00 roll, where the save versus petrified is spelled out. So too the 91-95 roll, and the save versus being blinded.
Enlarge or shrink, with no save, for the wand's wielder
The wand splits that spell's magical effect into two discrete effects so that it either enlarges or shrinks the caster (or target) without the caster getting to choose. When you cast the spell, the caster chooses, but with the wand casting "as if you had" then the wand / die roll chooses. Usually, when a caster casts Enlarge Reduce on themselves, they don't role a saving throw against that spell because they want to enlarge or reduce: they are not an unwilling target1.
"As if you had" means that the wielder grows or shrinks if the target can't be affected by the spell - that spell effect backfires on the wand's wielder.
The general case for this wand is:
"If the effect causes you to cast a spell from the wand, the spell’s save DC is 15."
This wording also avoids a fizzle.
Since the wand has variable results, the wielder could be trying to cast a spell at something that is not an eligible target creature. (Even though the wand's results are always driven by a die roll ...) In the case of this roll, 50-53 on the d100 roll (or 66-69 for shrink), in a situation where the target is an ineligible object or creature, the spell would otherwise fizzle if the wand description says "you cast Enlarge Reduce." (As it says for haste, faerie fire, etc).
This change in language telegraphs an intent: if what you are aiming at can't be enlarged or reduced, then the spell is cast on the wand's wielder.
Note: this wand and the Wild Magic Sorcerer subclass's Wild Magic feature have some very similar results when triggering the magical effect. If one looks at this item and attempts to capture the spirit of the item, and the chaotic nature of the outcomes, rather than beating the semantics out of it, I think the interpretation becomes clearer. Your grow or shrink, Alice. (And if a white rabbit shows up, so much the better!)
Each other casting listed will otherwise adhere to casting rules, since "you cast the spell, and save DC is 15" is the overriding guidance. The rolls 50-53, and 66-69 are uniquely tied to Enlarge/Reduce with no saving throw.
1 Enlarge Reduce spell text excerpt
You cause a creature or an object you can see within range to grow
larger or smaller for the Duration. Choose either a creature or an
object that is neither worn nor carried. If the target is unwilling,
it can make a Constitution saving throw. On a success, the spell has
no effect.
If the target is a creature, everything it is wearing and carrying
changes size with it. Any item dropped by an affected creature returns
to normal size at once.