"A modal verb is a type of verb that is used to indicate modality – that is: likelihood, ability, permission, request, capacity, suggestions, order, obligation, or advice. Modal verbs always accompany the base (infinitive) form of another verb having semantic content."- Wikipedia
This is an idiomatic construction. '[Noun]+को [verb-infinitive] है' is used to mean either '[Noun] has to [verb]' or [Noun] wants to [verb]'.
For example, नेहा को खाना है which means 'Neha wants to eat' or 'Neha has to eat' depending on context.
मुझे is essentially मैं + को.
Assuming you meant the second sentence to be 'mujhko delhi jana hai', there is no difference. Some people use मुझे and others use मुझको depending on personal preference. There are some who insist that मुझे is the correct form and मुझको is a colloquialism though.
It's the same with उसे/उसको, हमें/हमको, तुम्हें/तुमको etc.
मुझे is not 'have to'. It roughly corresponds to 'to me'.
The whole sentence with verb-infinitive+है is what ends up meaning 'have to'. For example, compare the given sentence with नेहा को दिल्ली जाना है (Neha has to go to Delhi).
However, this construction is idiomatic and the sentence cannot be literally translated into English.