The two states use different names for the same general offense. Missouri uses 'Driving While Intoxicated' (DWI) under RSMo § 577.010. Illinois uses 'Driving Under the Influence' (DUI) under 625 ILCS 5/11-501.
The substantive laws differ in important ways. Missouri has no per-se threshold for marijuana. Impairment must be proved through totality of evidence. Illinois has a per-se 5 ng/mL THC threshold for cannabis DUI. Both states use 0.08% BAC as the alcohol per-se threshold.
License consequences differ too. Missouri's administrative hearing is requested within 15 days of arrest. Illinois's statutory summary suspension is challenged through a Petition to Rescind within 46 days.