The easiest way is to break down the two terms:
Self Employment means you are responsible for declaring your taxes, managing your business, and deciding what work you do, and when and how you do it. If you’re self employed you won’t be entitled to holiday or sick pay. You can work for more than one client. You might be a sole trader, or you might be a partner in a partnership.
A sole trader is a self-employed person who is the sole owner of their business.
In summary, there isn’t really a difference between being a sole trader and being self employed – sole trader describes the structure of your business, whereas self employed shows that you don’t work for an employer or pay your taxes through PAYE.