There is a difference, especially when you add some modifier to the softbox. The umbrella, as I said in my previous post, is generally a soft, large light source. But, adding a grid, louver, mask etc can change the quality of the light. Plus, if you have a softbox that takes baffles, you can change the feathering effect (center brightness and gradial change outward).
And, as a light source is softer the larger and closer it is to the subject, the softbox excels here. With an umbrella up close, you will have a lot of spill onto the background. With a softbox, you can barn door the edge, grid the face, and gobo the background, making the light source aim only at the subject.
Plus, with some softboxes, you can put the light inside it, aiming at the front or back (towards or away from the subject) to change the quality of light on the subject. You can also gel a light source in a softbox to produce light which gradients from color to white where an umbrella would not be able to accurately reproduce this effect.