- Сюди́ = в це мі́сце 'to this place', it indicates a direction. It is an answer to the question «куди?» 'where? to what place?'.
- Тут = в цьо́му мі́сці 'in this place', it indicates a location. It is an answer to the question «де?» 'where? in what place?'.
Сюди is similar to the archaic English word 'hither'.
Is the only difference between ідіть and йди formal/plural "you" and singular/familiar "you"?
Yes, ідіть/йдіть is plural, іди/йди is the singular.
The versions with й are preferred after vowels, versions with і are preferred after consonants.
My mrs uses "Idi Syuda!" when she is angry at me. I am not sure this sentence has the exactly same meaning as in its literal sense :-)