The radical is chemical species with unpaired electrons and oxidant capacity. The ligands are Lewis bases having electron pairs for coordinating metals.

The radical is chemical species with unpaired electrons and oxidant capacity. The ligands are Lewis bases having electron pairs for coordinating metals.

In the case of the paper discussed above, ligand is coordinated to a metal center. Ligands coordinated to metals can be classified as innocent and non-innocent ligands. Innocent ligand is where ligand assumes a definitive oxidation state. When ligand is non-innocent (non definative oxidation state),  oxidation takes place at the ligand (even in case when it is coordinated to a say a metal center) resulting in radical ligands. Nitrosyl (as in case of the paper) is a typical radical ligand.

In the article you cite, the ligand, as is usually the case, is bound to the metal by donating electron pairs.  However, in this specific case, they designed the organic framework of the ligand to have unpaired electrons, hence the ligand is a radical.  They are trying to determine if interaction between the ligand unpaired electrons and the metal can have an effect on the chemistry.

The discussion does not make any sense if the term "ligand" is not clearly defined.

Use the definitions recommended by IUPAC:

http://goldbook.iupac.org/

At least read

https://en.wikipedia.org/wiki/Ligand

Quick comment: " I definitely know the difference between ion and radicals" I'm afraid you do not know. There  are numerous example of ion-radicals

Someone downvoted my comments.  What is wrong? If you downvote, explain why.

Dear Prof. Geletii,

I've not downvoted your answer. If I've seen your comment earlier, I would definitely not have downvoted it, because you're comment clarifies lot of confusion of mine, and you're  correct. I didn't know about radical ions as you've suggested(https://en.wikipedia.org/wiki/Radical_ion#Radical_anions). I've asked the question based on common textbook definitions.

Now I feel stupid for my ignorance.

Can you suggest any articles/books/papers which give more in depth review on these topic? Thank you for the answer. 

There is no general definition for the "ligand". This causes numerous confusions

IUPAC definitions:

ion

An atomic or molecular particle having a net electric charge.

radical ion

A radical that carries an electric charge.

radical (free radical)

A molecular entity such as .CH3 , .SnH3 , Cl. possessing an unpaired electron. (In these formulae the dot, symbolizing the unpaired electron, should be placed so as to indicate the atom of highest spin density, if this is possible.) Paramagnetic metal ions are not normally regarded as radicals. However, in the 'isolobal analogy' the similarity between certain paramagnetic metal ions and radicals becomes apparent. At least in the context of physical organic chemistry, it seems desirable to cease using the adjective 'free' in the general name of this type of chemical species and molecular entity, so that the term 'free radical' may in future be restricted to those radicals which do not form parts of radical pairs. Depending upon the core atom that possesses the unpaired electron, the radicals can be described as carbon-, oxygen-, nitrogen-, metal-centred radicals. If the unpaired electron occupies an orbital having considerable s or more or less pure p character, the respective radicals are termed σ- or π-radicals. In the past, the term 'radical' was used to designate a substituent group bound to a molecular entity, as opposed to 'free radical', which nowadays is simply called radical. The bound entities may be called groups or substituents, but should no longer be called radicals.

A ligand can be neutral entity, ion, radical, or ion radical.

Dear Prof. Geletii,

Thanks for the clarification. Now I get the complete picture.