Featured Not a rock hound please help ID this stone

Different folks seem to have different terminology, and terminology may vary in other languages. But in mineralogical terms, in English, agate is simply one variety of chalcedony. No more, no less. All agates are chalcedony, but not all chalcedony is agate.
Most rockhounds would be happy to refer to this inclusion as either agate or chalcedony. Most or many agates are banded when cut and polished, and many are grey; such as Botswana agate. See https://en.wikipedia.org/wiki/Agate for some discussion of types of agates and their formation process.
The rock in AJ's second photo would be identified by most rockhounds and mineralologists (in the US) as a variety of chalcedony commonly called agate; very similar to Botswana agate, though online that specimen appears to have been identified as "Chalcedon" by a museum in Prague.
(In English, "chalcedony is the mineral; "Chalcedon" was a city in the Byzantine Empire. Not so in other languages, however.)


Botswana agate

 

My problem with chalcedony is that I am a theologian with a bad memory. The only way for me to remember the name of the stone, is to think of the Council of Chalcedon of 451 AD, in which the nature in Christ (man-God) was discussed. It was significant because it led to a schism.
When thinking of the rock, I am so happy I get as far as Chalcedon, that I often forget to add the y.

I think in general we Europeans are more strict when it comes to mineral terminology. Probably because we are influenced by 'mineral kingdom' Germany. Germans are known for their precision.
My mother was a rockhound, and we often visited the German mineral capital Idar Oberstein. This is a 1997 stamp to commemmorate 500 yrs as a gem region (Edelsteinregion):

 

Yes, I understand. I'm trying to point out that a discussion of the name of this item is dependent on location and language, and whether one is talking to a rockhound, jeweler, or mineralologist. In the US, most rockhounds would prefer to specify the type of chalcedony: agate, jasper, carnelian, etc.....rather than using the more general term.

Terminology is endlessly fascinating, and one can get caught by regional differences.....one could just specify the chemical makeup and the crystalline structure ; they're all silicon dioxide but that is pretty meaningless to a layperson, though very precise.
Much like a discussion between a Londoner and a New Yorker as to whether a tree is a plane or a sycamore. One could just specify "Platanus species" and call it good.
(Which reminds me, that the green portions of the rock might technically be Mtorolite, a green chalcedony, which might point to origin in Zimbabwe.....)

 

I probably didn't explain it well, because it is the same here, except that we usually call the grey chalcedony: chalcedony. Which is probably why the museum in Prague called the grey chalcedony chalcedon, which is the Czech word for chalcedony.
Once other minerals appear in chalcedony and change the 'basic' grey colour, we specify agate, jasper, carnelian, etc.
By the way, carnelian is almost as important here in The Netherlands as Mediterranean red coral, so anyone who doesn't call it carnelian is frowned upon.
Traditional Dutch carnelian necklace, 14k gold clasp:

 

The green part looks like varicite but it is more likely chrysoprase because the whitish part looks like some type of agate and both are different types of quartz.