if you claim to be domiciled in Illinois (Domicile (Home of Record) - The place an individual intends to be his/her permanent home; a place that he/she intends to return whenever absent. A domicile, once established, continues until the individual moves to a new location with the true intention of making his/her permanent home there. An individual can only have one domicile at a time)  IE you intend to return after your stint in MO you are a full-year Illinois resident.

for Misssouri, you don't meet its definition of non-resident so you would be a part-year resident.

the result: you file a Mo return as part-year resident only reporting your income earned there. this return must be prepared before Illinois.  for Illinois yo pay tax on the MO income and then get a credit for the income taxed by both Il and Mo.