Formation of Ion

An ion is an atom or group of atoms carrying positive or negative charge. Example Ca²⁺, O^2-, SO₄^2- etc.
If a particle has equal numbers of protons (+) and electrons (-), the particle charge is zero, and the particle is said to be neutral.
In a chemical reaction, electron(s) can be transferred from atom to another atom.
If electron(s) is removed from an atom, the number of protons will be more than number of electrons. In this case, the atom will has excess positive charge and hence form a positive ion (cation).
(An atom losses electron to form positive ion)
If an atom gains electrons, there is an excess negative charge in the atom, so a negative ion is formed.
In other words,

The atom losing electrons forms a positive ion (cation) and is usually a metal.
The atom gaining electrons forms a negative ion (anion) and is usually a non-metallic element.

(An atom gain electron to form negative ion)

Difference Between an Atom and an Ion That Have Same Electrons Arrangement

After forming an ion, the electron arrangement of the ion is similar to the noble gases.
For example, the electron arrangement of fluoride ion is 2.8 which is similar to a Neon atom, 2.8.
Fluoride ion and the neon atom have similar electron arrangement.
Fluoride ion carries charge whereas neon atom is neutral.

(The electrons arrangement of a fluoride ion is the same as a neon atom. However, they are so much different chemically)