There are between 20-40 low-cost airlines in Europe. Some low-cost airlines are much bigger and popular than others and fly everywhere in Europe, while others are smaller and have a limited choice of flights. All of them share one thing: they made traveling affordable to so many people and now flying between two countries in Europe is almost as easy as taking trains or buses between two cities.
You're not crazy for thinking that a flight price has changed after searching it a few times in your web browser. Based on the cookies in your browser, flight prices do increase when a particular route is repeatedly searched, as the site wants to scare you into booking the flight quickly before prices get even higher. Always search for flights in incognito or private browsing mode to see the lowest prices.