I'm not sure I understand your post. When you search for fares on an airline website, you're using their algorithms to obtain a certain set of results based on certain parameters which are shown in some order that's set by the algorithm (and according to your filters and preferences). Third party sites have their own algorithms (using their own parameters, sometimes including impossibly short but legal connection times) and they can cobble up fare results from code-share airlines that you wouldn't necessarily see on one airline website because they don't have integrated systems that sell each other's tickets. There is a substantial overlap between airline and third party search results, but it's the area where there is no overlap that gives third parties a reason to exist (otherwise, they'd just be replicating the airline's own search results and that has zero value to anyone). Also, third party sites package fares with hotels and rental cars so you're not comparing apples to apples, since airline websites only sell airline tickets. It sounds like you have little competition for your airport if you have a single "go to" airline.
I've used both airline and third party sites and can attest that you can get substantial savings using a third party site. But it always depends. It's not true of every itinerary or every airport. You have a better chance when you live near an airport(s) that have a lot of competition on a particular route. It's worth comparing both, and knowing the pros and cons of using third parties versus airline sites.