Well, the two are actually very different if we are talking about their accepted definitions.
An assessment is like a test, or an exam. It can also be an evaluation. In an assessment, you take things you have observed, and you come to a conclusion about those observations. An example would be a school assessment. A teacher will give a student a type of test in order to see if the student has learned what the teacher has taught. Using the student's answers, the teacher can determine what the student understands, and what the student doesn't.
A prediction, on the other hand, is based on what someone *thinks* or *believes* will happen. That person has come to a conclusion, but it isn't based on the same kind of observation. Usually, people do make predictions based on patterns, or what has happened in the past, but that conclusion won't necessarily happen.
Here's an example of a prediction. Let's say that the same teacher from earlier takes all her students' test results for the last 5 years. She looks at what has happened in the past, and she "predicts" that 60% of her students will pass this test this year. She doesn't know if her prediction will be right, but she is making a prediction based on a pattern.
The biggest difference is that, in an assessment, someone is taking evidence from an event and making a conclusion about that one event. A prediction is making a "guess" conclusion about an event that hasn't happened yet.
Hope this helps!