What is the difference between solid modelling and surface modelling?

The short easy answer is that with solid modeling, forms are built-up by drawing outlines and protruding them into forms, as well as using other protruded outlines to cut forms. Often these shapes are more geometric overall, and solid modeling is usually used to create the internal details of products. SolidWorks is a solid modeler (but can create surface forms too)

Surface modeling develops shapes by stretching a "surface" between 3d curves that you individually create. With it you build forms by creating one small surface at a time, slowly creating the complete shape. The intersections between the surfaces are very controlled so they can be very very smooth or crisp like a crease. Usually the shapes are more freeform and sleeker than an object that was created with solid modeling, but some people are very good and the lines blurrr.. Alias is a surface modeler, but Solidworks can create shapes with surfaces too

olids modeler: Starts with a solid object. You add and subtract other solid objects to it. If you cut into it, you're left with your solid object minus what was cut out--just like in the real-world. It's all very rational.

Many solids modelers are "parametric" meaning you can go back and look at the list of commands you've executed since the start of your model (the "construction tree") and change anything (hoping your model doesn't "break.") Very useful!

Pro/E and Solidworks are the most popular.

Surface modeler: A bunch of infinitely-thin membranes defined by boundary curves. If you want, you can connect one membrane to another, creating a "water-tight" form that looks solid, but if you cut into it, it would be hollow and you'd have to patch the missing cutout piece (intersect tools are typically used to automate this.)

Surface modelers generally aren't parametric. There is no construction tree. It's very hard to change something you did and expect the rest of your model to update.

Why would you use a surface modeler then? Because it's more freeform, and historically, the tools have allowed you more control over the shapes of those "membranes" than if you were using a solids modeler. And because designers have been attracted to this, the user-interfaces tend to emphasize the freeform more than the solids-modelers, which cater to engineers.

Alias and Rhino are the most popular.

there are some other differences like parametric history and assemblies as well that make Solidworks a worthwhile software to complement your Alias skills...