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When NH3 was alone, it was having a lone pair on nitrogen. An electrophile H+ attacked this lone pair to form a coordinate bond with nitrogen. It formed a (+)ve charge on nitrogen in NH4.
There is actually a coordinate bond (which is actually a kind of covalent bond in which only one of the participating atoms donate both of their electrons to form a covalent bond) between lone pair of nitrogen in ammonia(NH3) and a proton(H+ ion),which hence creates an ammonium ion(NH4+).
Further this ammonium ion due to a positive charge forms an ionic bond with chloride ion(Cl–).
So actually there are:-
three pure covalent bonds in NH3.
a coordinate bond(which is also a covalent bond) between NH3 (ammonia)and H+ ion(proton).
And of course an ionic bond between NH4+ (ammonium ion) and Cl–(chloride ion)