There are more than sixty different beef cuts in the meat case today. Add in the fact that many cuts have several different names and the meat case can be very confusing.
And a steak may be labeled a certain name in one area of the U.S., and the same labeled name in another area might be a completely different cut of steak.
In my area, Southeast Missouri, a Delmonico steak was a Boneless Top Sirloin beef steak.

In other parts of the country, a Delmonico was was a Bone-In Top Loin Steak (cut from the short loin), or a Rib-Eye Steak (cut from the rib).

So, unless you know if the Delmonico steak you have had before was cut from: the Short Loin, Sirloin, or Rib, it's hard to tell exactly what you have eaten before as a Delmonico steak.
You could possible look at the above three choices labeled as such in the grocery's meat case, and see if one of those "looked" like what you had before. If so, then go with that one.
I know this wasn't a quick easy answer, but there really isn't one. But I hope this sets you out on the right path.