They are "to sell" in meaning and I think we use them in different cases but I don't know. Can anybody help me???
売る is more colloquial and a bit more general. For example it can be used metaphorically e.g. こいつ魂を売ったな. 販売 is more formal and specific and refers to selling, normally goods. You can't say こいつ魂を販売したな!
売る is more general form for selling. 販売する is used referring to sale of goods, and specifically to customers who are already are seeking to buy the goods. As another example of something that falls under 売る, there's 営業する which is trying to sell goods or services, to customers who could potentially buy the goods or services. So as an example car salesmen working in a car dealership would be 販売員, whereas car salesmen visiting potential customers directly would be 営業員.
My answer is really just adding onto the others. What they both said is good information. Think of it kind of like this...you know how both 'to buy' and 'to purchase' mean the same thing in English, but have a different feeling because of how and when they're most often used? It's very similar to that. Casually, we say buy, but it's also not rude to say buy in a formal situation, however businesses almost always use 'purchase' because it has a more formal sound to it? And we don't often say 'purchase' amongst friends? It's remarkably similar to that. 売る is just straight up 'sell' and 販売する sounds more like 'the commercial-level sale of goods or services from a business'.