AI engineer is more of a software engineer where as a Data Scientist is more of a researcher! In any discipline scientist makes a discovery whereas an engineer is responsible for implementing it on a practical scale or for mass production.
So for example, an e-commerce company is interested in segmenting their customers, a data scientist will pave way in identifying the features / alogirthms that work best whereas an AI engineer will be responsible in deployment of the ML model building and prediction process in order to make real time predictions.