What's the difference between "licensing" and "licensure?"

In each of your examples licensing is used as an adjective, while licensure is used as a noun.

Licensure:

NOUN

[MASS NOUN] chiefly North American

The granting of a license, especially to carry out a trade or profession.

The suffix -ure creates an abstract active noun:

suffix forming abstract nouns of action,

from Old French -ure,

from Latin -ura, an ending of fem. nouns denoting employment or result.

Licensing is the progressive form of license, used as a verb, noun or an adjective, depending on the context:

• All the progressive conjugations are verbal uses of licensing

The Board for Professional Engineers has been licensing engineers for 4 decades.

• As a present participle, licensing is used as an adjective.

The Board for Professional Engineers is a licensing body.

• As a gerund, licensing is used as a noun.

The Board for Professional Engineers arranges the licensing of engineers.