What is the difference between a regular company and a limited company?

I can only answer from a UK perspective, but here the difference is mainly to do with ownership.

A 'normal' company is classed as a sole trader and so the money of the company and the owner are seen as the same. If the company gets into debt or is sued, the money can be taken from the company and the owner. So the owner could lose their house, personal savings etc. The benefit of being a sole trader is that the legal requirements are pretty straight-forward so it is easier to keep accounts and complete tax returns.

A limited company means that the company and the owner are separate. Debts can only be paid from the money the company has - the owner cannot lose their private property. The downside to a limited company is that it is often more expensive to run, as there are more legal requirements, such as accounts need to be published and audited. It can be more tax efficient to run a limited company though.