the difference between shaving soap and saving cream
Different products produce different foams, which have other characteristics.
Shaving creams are usually softer and lather easier. They are usually more hydrating and so better for people with dry skin. They don't last as long as shaving soap. They are smaller in volume than your aerosol, but you only need around an almond size amount to produce enough lather for several face and head passes. They last longer than the compressed canister gel you are likely currently using.
Shaving soaps are harder and a little trickier to lather. They last for ages (seriously, you will easily get three months of daily shaves out of a 4oz soap). However, since they are soaps, they will generally strip all of the natural oils from your face, leaving it very dry. People with oily skin won't mind. Often, other stuff is added into account for this.
Both soaps and creams are often supplemented with other helpful stuff. Things like Vitamin E essential oils can help skin protect itself and keep it healthy. Many creams have added Glycerin, which will soften hair and make it easier/smoother to cut.
Since they are very simple to create, there are often fewer chemicals and more natural ingredients which your skin might appreciate. But also, your skin might not care at all, and there are definitely a lot of creams and soaps absolutely pumped full of harsh, industrial-grade chemicals.
Finally, a lot is scented with all kinds of stuff. There is also the availability of artisan and small-batch soaps using all-natural ingredients, etc.
This is a little bit like asking what the difference is between a jar of supermarket instant coffee and artisan roasted coffee beans. Both will give you that caffeine injection, but some will taste better than others, and some might be healthier/more sustainable.