I'll be at my uncle's house just in case you need to reach me.
I'll be at my uncle's house should you need to reach me.
Could you tell me what is the difference between those?
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In the given context, there's no difference. They mean the same.
'just in case' is the idiom used to mean -in the event that (something happens) i.e. in that condition
should is also used as 'if' and thus, this word too talks about the condition -in the event that/if something happens.
should -expresses a condition i.e. just in case!
But of course there is a difference but not in answering but in asking. :) Let me alter the sentences somewhat to clarify meaning. In case: I go to my uncle's house anyway - so I'll be there if you need me and I'll be there if you do not. If: I stay here but will go to my uncle's house when and only when you need me, and if you don't need me then I remain at home..