They are very different.
Compare a single letter from each side, don't look at the entire word or layout. Enlarging the pics on the auction you can see the occasional burr at the end of a cut. Not the standing metal from an impression stamp but a tiny ragged burr here and there.

You really don't have to go any farther than the F to see that they are different if enlarged & examined closely.
The downstroke cut of the main stem of each is different.
The right side action lettering, the stem backside is not quite completely squared off by the bottom cap. The left side is with the forward side of the cut still visible in the cap cut.

On the right side, the top cross cut of the F is weak/thin with the very forward portion taking a downward turn to the serif.
The left side is a deeper cut and straight accross.
The bottom cap on the right side has angled ends, nearly the same angle that the lettering stands.
The bottom cap on the F on the left side has ends that are squared with the cap itself forming a rectangle.
Tiny differences but things that would not show if they were rolled with an identicle die.

The G on the right side has a nice big burr hanging on the bottom/end of the verticle cut. Not from a die,,from a graver. You have to enlarge the pics to see it probably.

Differences in the curves of the S are easily seen in the pic above.
On the left side, the inside loops are not identicle as they are on the S engraved on the right side.
S,O,D,B,ect are the difficult letters to cut for most engravers, Even more so when called upon to make a matching pair.

That they do look so much the same is good. That's one goal of hand lettering especially when it's being duplicated as it is here.
A prepared pattern was most likely used if more than one was being cut. If not then one side is layed out and cut, then a pull is made of that and layed down on the otherside.
You don't lay it out again from scratch on the opposite side. That usually leads to many small errors that really show up when viewed. Takes too much time too.

JMHO of course,,