Question

Hydrogen bonding is of two types - $t$ Intramolecular and intermolecular Am I right ?

Answer 1

Nope. It is only intermolecular.

It is just a misnomer that we call it "hydrogen-bonding". Yes, the hydrogen is bonded within the molecule, but the term "hydrogen-bonding" does not refer to that.

It refers to the polarizing interaction with an electronegative atom on another molecule, which strictly speaking, is a significantly weaker interaction than in a regular bond.

This interaction is...

the polarization of electron density from an adjacent molecule's $H$ atom by an electronegative-enough atom.

Often we speak of $O$, $N$, and $F$ NOT bonded to the $H$ in question as being hydrogen-bond acceptor atoms. The electronegative atom BONDED to the $H$ atom is then the hydrogen-bond donor.

Thus, there is particularly noticeable hydrogen-bonding in $N{H}_3$, $HF$, and $H_{2}O$ samples.

It is not, however, restricted to $N\cdots H-N,O\cdots H-O,andF\cdots H-F$ interactions. Chloroform and acetone are also known to weakly hydrogen-bond.