What do atomic radius and ionic radius mean?

Atomic radius is the distance from the center of the nucleus to the outermost shell of electrons in an atom. It measures the size of an atom.
For metals,it is the metallic radius,defined as half the internuclear distance between two adjacent metal atoms in a metallic crystal. For example,the internuclear distance in solid copper is $256 \, pm$,so the metallic radius is $\frac{256}{2} \, pm = 128 \, pm$.
For nonmetals,it is the covalent radius,defined as half the distance between the nuclei of two atoms bonded by a single covalent bond. For example,the distance between two chlorine atoms in a $Cl_2$ molecule is $198 \, pm$,so the covalent radius is $\frac{198}{2} \, pm = 99 \, pm$.
Ionic radius is the effective distance from the center of the nucleus to the outer shell of an ion. Cations are smaller than their parent atoms due to the loss of electrons and increased effective nuclear charge (e.g.,$Na^+$ is $95 \, pm$ vs $Na$ is $186 \, pm$). Anions are larger than their parent atoms due to increased electron-electron repulsion and decreased effective nuclear charge (e.g.,$F^-$ is $136 \, pm$ vs $F$ is $64 \, pm$).