Learn English – “Verity” vs. “veracity”

Yes, conterminous and coterminous both mean "to share a boundary".

According to the entries for co- and con-, below, co- is an Anglicising of con-, which is possibly why Latin purists prefer con-

In this instance co- and con- both mean together or with.

Etymology of co-

in Latin, the form of com- in compounds with stems beginning in vowels and h- and gn- (see com-). Taken in English from 17c. as a living prefix meaning “together, mutually, in common,” and used promiscuously with native words and Latin-derived words not beginning with vowels, sometimes even with words already having it (e.g. co-conspiritor).

Etymology of con-

prefix meaning "together, with," sometimes merely intensive; the form of com- used in Latin before consonants except -b-, -p-, -l-, -m-, or -r-. In native English formations, co- tends to be used where Latin would use con- (e.g. costar).

For the most part, they are used in different contexts.

• Field is most often used to designate a domain of professional specialization: you would speak of an attorney in the field of patent law, a doctor in the field of pediatrics, or a scholar in the field of Middle English literature. You might say that someone that is in the legal or medical or LitCrit field if you had only a vague idea of what specialization he pursued—“He’s something in the medical field”—but you would not do so if you had already implied that larger domain: ^✲“He’s a surgeon in the medical field”. You would not, except for humorous effect, use the term with a non-professional: a ^✲“machinist in the aeronautics field”, a ^✲“secretary in the legal field”, a ^✲“merchant in the medical-supply field” (though you might speak of an “aeronautical machinist”, a “legal secretary”, a “medical-supply merchant”).

• This invidious distinction is not observed with industry, which designates a domain of commercial endeavour and embraces para-professionals, businessowners, managers, technicians, skilled labourers, support staff, and unskilled workers as well as professionals. It is typically used to designate the “supply chain' for particular classes of product: the steel industry, the energy industry, the entertainment industry, the education industry, the financial-services industry. The term is mostly used statistically and is not ordinarily applied to individuals, except in relation to industry-wide conditions: “Joe's in the construction industry and having a hard time finding work“ is OK, but not “Joe's a manager in the construction industry”.

• Sector is similar to industry but is usually employed to distinguish domains on a structural rather than input/output basis: the public and private sectors, the non-profit and for-profit sectors, the manufacturing and service sectors. Its use is almost entirely statistical; you rarely speak of an individual as being in this or that sector, except when you speak of an individual moving from one sector to another, as when a defeated congressman becomes an industry lobbyist.

None of these distinctions is hard-and-fast. An insurance agent, for instance, may claim professional status by describing himself as working in the field of personal protection. Industry may come in handy in a bio or resume to describe an individual's varied career: “I have held responsible positions in every aspect of the housing industry”. Sector may replace industry when speaking narrowly of a particular aspect in which different domains are compared: for instance, an analyst may contrast the performance of the construction, manufacturing and service sectors on the stockmarket or in creating jobs.