The peneplain part is important because it means you have to know something about the erosional history of the feature: how it came to be, not just what it looks like. But, the idea of a peneplain is tied to an outdated theory of landscape evolution that contemporary geologists have abandoned.

A monadnock is a geographic feature. Def:

an isolated hill or ridge or erosion-resistant rock rising above a peneplain.

The American Geosciences Institute Glossary of Geology—a definitive source I'd rely on as a geologist—includes both a temperate climate and the necessity of rising conspicuously above a peneplain, not just a flat area, in its definition. 🧵

To contrast with the New Zealand (or at least mountainous) #geomorphology that I usually post, here is a spectacular geomorphic scene from far west Queensland. #photo #bigsky #peneplain ⚒️ #geoscience #geography #Australia #biodiversity #gibber #geology

Ship Rock must be by far the geologic feature most often mistaken for a monadnock (which is a humid temperate climate landform rising above a peneplain). It’s an exhumed volcanic neck.

geoinfo.nmt.edu/tour/landmar...

Thinking here about poorly understood eastern England in the late Miocene to early Pleistocene, uplift in the Pennine chain converts probable peneplain into bypass zone and deepening North Sea basin into sink zone, with gradual n'wards extension of deltaic sedimentation across southern N Sea bight.

Barclay Mountain as seen from Lamb’s Park outside Canton, PA.
Not so much a mountain as a plateau or peneplain, like most of the hills in our beautiful state.

Nice photo of an amazing landform! Ship Rock is a volcanic neck, not a monadnock (which is an erosional remnant of resistant rock rising above a peneplain in a temperate, not arid, climate). But, that doesn't make it any less spectacular.

geoinfo.nmt.edu/tour/landmar...

I once described a period of low tectonic activity and peneplain development in a regional geological history as 'nothing much happened' to a prominent sedimentologist. I was promptly and permanently corrected.

So, in my opinion, Ship Rock doesn't satisfy the temperate climate or peneplain aspects of the AGI definition. You'd be much better off and absolutely correct to call it an erosional remnant and/or a volcanic neck (like they do in the NM Bureau of Geology link I posted).