Introduction:
In the field of chemistry, chemical bonds are the forces that hold atoms together in a molecule or compound. Different types of chemical bonds are formed based on the sharing or transfer of electrons between atoms. Kossel and Lewis are two renowned scientists who made significant contributions to the understanding of chemical bonding. In this case, they described both ionic and covalent bonds.

Explanation:
The four options provided in the question represent different types of chemical bonds. Let's discuss each of them in detail:

1. Metallic bond:
- A metallic bond is formed between metal atoms.
- In metallic bonding, the valence electrons are delocalized and move freely throughout the metal lattice.
- The attraction between the positive metal ions and the delocalized electrons results in a strong bond.
- Kossel and Lewis did not describe metallic bonds.

2. Polar covalent bond:
- A polar covalent bond is formed between two non-metal atoms with different electronegativities.
- This type of bond occurs when electrons are unequally shared between the atoms.
- The atom with higher electronegativity attracts the shared electrons more strongly, creating a partial negative charge.
- The atom with lower electronegativity has a partial positive charge.
- Kossel and Lewis did not specifically describe polar covalent bonds.

3. Coordinate bond:
- A coordinate bond (also known as a dative bond) is a type of covalent bond.
- It occurs when one atom donates a pair of electrons to another atom that needs them to complete its valence shell.
- The atom donating the electron pair is called the donor, and the atom receiving the electron pair is called the acceptor.
- Kossel and Lewis did not specifically describe coordinate bonds.

4. Ionic and covalent bond:
- Ionic and covalent bonds are the two main types of chemical bonds described by Kossel and Lewis.
- In an ionic bond, electrons are completely transferred from one atom to another, resulting in the formation of ions with opposite charges.
- In a covalent bond, electrons are shared between two atoms.
- Kossel and Lewis developed the octet rule, which states that atoms tend to gain, lose, or share electrons to achieve a stable electron configuration with a full outer shell of eight electrons.
- The concept of electron transfer and sharing in ionic and covalent bonds forms the basis of their theories.

Therefore, the correct answer is option 'D' - ionic and covalent bond. Kossel and Lewis extensively described these two types of chemical bonds in their work.