As I use the term, English only has one copula: the verb "to be". The object of a copula takes nominative case, not accusative, so "It is I" not "*It is me." (Although some people do accept this usage for some reason.) Also, in formal semantics, the copula disappears. So "John is a man" turns into something like "exists(x) {John(x) and man(x)"}
None of the other verbs on the list meets either of those tests. For example, we have to say "John smells him"; no one accepts "*John smells he." Semantically, "John smells a man" becomes "exists(x,y) {man(x) and John(y) and smells(y,x)}
I've heard of "psuedo-copulas," but none of my graduate-level linguistics classes had any use for the distinction. I suspect the modern notion of theta roles eliminated the need for a special category of pseudo-copulas. That is, we can specify that "to smell" is a transitive verb that can take either a noun phrase or an adjective phrase as a direct object.
Carnie has a good explanation of theta roles. Heim describes the copula in semantics.