Cordially vs Eagerly - What's the difference?

Cordially is a related term of eagerly.

is that cordially is in a cordial, warm or friendly manner while eagerly is in an eager manner.

(en adverb)

In a cordial, warm or friendly manner.

* 1893 , London, Royal Geographical Society, The Geographical Journal

I may ask you, then, cordially to thank Sir George Goldie for all that he has done for the Society.

* 1898 , Ivan Sergeevich Turgenev, Tourguéneff and his French Circle

My dear Monsieur Durand,—I am sending you[....]

Ever most cordially yours,

*:: Iv. Tourguéneff.

As indicated above, the term is often used in letter closings.

(en adverb)

In an eager manner.

* heartily, with a will