A type assertion asserts that t (an interface type) actually is a aType and t will be an aType; namely the one wrapped in the t interface. E.g. if you know that your var reader io.Reader actually is a *bytes.Buffer you can do var br *bytes.Buffer = reader.(*bytes.Buffer).
A type conversion converts one (non-interface) type to another, e.g. a var x uint8 to and int64 like var id int64 = int64(x).
Rule of thumb: If you have to wrap your concrete type into an interface and want your concrete type back, use a type assertion (or type switch). If you need to convert one concrete type to an other, use a type conversion.