What's the difference between gerund and gerundively?

Gerund

Definition:

(n.) A kind of verbal noun, having only the four oblique cases of the singular number, and governing cases like a participle.
(n.) A verbal noun ending in -e, preceded by to and usually denoting purpose or end; -- called also the dative infinitive; as, "Ic haebbe mete to etanne" (I have meat to eat.) In Modern English the name has been applied to verbal or participal nouns in -ing denoting a transitive action; e. g., by throwing a stone.

Example Sentences:

(1) A gerund is a verb ending in -ing that acts as a noun: I like swimming, smoking is bad for you, and so on.
(2) A research on the acquisition of morphemes of plural, diminutive, augmentative, gerund, imperfect, and preterite with 109 Spanish children from 3 to 6 is reported.
(3) Thirty years on from the riots, one walks up Prince's Avenue, past what was the incinerated Rialto and the sign into Toxteth, and yet another sign promising imminent arrival into the "Regeneration Zone", and showing pictures of a perfect cereal-packet multiracial family, pristine modern houses and beautifully refurbished original stock – beneath which is the inevitable crass slogan that accompanies every corporate or political effort these days, always beginning with a pretentious gerund, in this case: "Creating neighbourhoods for the future".
(4) Four hundred and twenty-seven deaf students (age 10 to 19 years) and 60 hearing children (age eight to 10 years) judged the grammaticality of sample sentences which contained infinitival or gerundive complements.
(5) 7 Don't fear the gerund Geoffrey Willans and Ronald Searle's guide to life at St Custard's school , How to Be Topp, features a cartoon in which a gerund attacks some peaceful pronouns, but it is nothing to be afraid of.

Definition:

Example Sentences:

(1) A gerund is a verb ending in -ing that acts as a noun: I like swimming, smoking is bad for you, and so on.
(2) A research on the acquisition of morphemes of plural, diminutive, augmentative, gerund, imperfect, and preterite with 109 Spanish children from 3 to 6 is reported.
(3) Thirty years on from the riots, one walks up Prince's Avenue, past what was the incinerated Rialto and the sign into Toxteth, and yet another sign promising imminent arrival into the "Regeneration Zone", and showing pictures of a perfect cereal-packet multiracial family, pristine modern houses and beautifully refurbished original stock – beneath which is the inevitable crass slogan that accompanies every corporate or political effort these days, always beginning with a pretentious gerund, in this case: "Creating neighbourhoods for the future".
(4) Four hundred and twenty-seven deaf students (age 10 to 19 years) and 60 hearing children (age eight to 10 years) judged the grammaticality of sample sentences which contained infinitival or gerundive complements.
(5) 7 Don't fear the gerund Geoffrey Willans and Ronald Searle's guide to life at St Custard's school , How to Be Topp, features a cartoon in which a gerund attacks some peaceful pronouns, but it is nothing to be afraid of.