The difference is in way we observe some object that is moving. In translatory motion each point of the object has to go in straight line. A ball for example when kicked is rolling which means that not all of its oints are going in straight line. Some of points on ball are rotating. On the other hand in rectilinear motion it is only important that object is moving on straight line and it doesnt matter if it is rotating. So kicked ball that moves on ground is example of that.
Example of translatory motion can be our body in a bus that is going in straight line but not that wheels are rotating so they are moving rectilinear.