Infinitive without to

What's the difference between" You need stay at home" and " You need to stay at home"? It seems to me that the former one talks about things that someone ought to do as responsibility. Yet, the latter one talks about things that someone needs to do in the future, not at the present. Would appreciate it if someone could help.

• *You need stay at home is an ungrammatical sentence.

Need, like dare, is a semi-modal verb. That means it can act like a Modal Auxiliary verb in certain situations, of which this is not one. When it does act like a modal auxiliary verb, it can take an infinitive without to; that's what modal auxiliary verbs like must, can, and would do:

• You must stay at home; she can stay at home; I would stay at home.

So, when do semi-modal verbs get to act like modals?
In negative contexts. Semi-modality is a Negative Polarity Item, like ever or budge

• He sat down and didn't budge for an hour, but not *He budged for a while
• He doesn't ever go down there, but not *He ever goes down there
• You need not stay at home, but not *You need stay at home
• He dare not tell the story, but not *He dare tell the story

When semi-modals don't occur in a negative environment, they just take infinitives with to, like most verbs; it's only with negation that they do tricks.