The core difference is that while Automated Machine Learning can help you make a prediction for a particular point in time (e.g. today), Automated Time Series can help you build a series of predictions (a forecast) for results for a period of time into the future. With Automated Time Series you create time-aware models to predict future events while training those models on past data.
A major difference between time-aware and conventional modeling is in how validation data—used to judge performance—is selected. For conventional modeling in our Automated Machine Learning product, rows are selected from the dataset for validation, without regard to their time period. This practice is modified for time-aware modeling in Automated Time Series to prevent validation scores that are overly optimistic and misleading (and potentially lead to damaging conclusions and actions). Time-aware modeling does not assume that the relationship between predictors and the target is constant over time.
Here's a simple example using Automated Time Series. Let's say you want to forecast housing prices. You have a variety of data about each house in your dataset and plan to use that data to predict the sales price. You will build a model using some of the data and make predictions using other parts of the data. The problem is, randomly selecting sale prices from your dataset suggests you are randomly selecting across time as well. In other words, the resulting model doesn't predict the future from the past. Using time-aware modeling, you can train and test models using time-based folds, which assures that your models are always validated on future house price data (the purpose of your forecast). It isn't necessary to use the most recent data to make predictions—only to use data that is more recent than the data used for model training—to ensure that model predictions about the future hold up.
Other potential use cases for Automated Time Series can be seen in this other post. If you think this is something you might like to add, please talk to your account team.