The words in general terms are closely related, "a serial list of items forms a series" for example. However they are essentially only loosely related terms when applied to television.
Series. A TV show broken into groups of episodes. Each group is usually broadcast at a regular (often weekly) interval or released simultaneously on streaming services. Each group is released with a significant gap between each. In the USA each group of episodes is called a season, in the UK each group is what is called a series.
Serial. When the story arc of any episodic content spans multiple episodes (of television, but can also be applied to magazine stories or comics for example).
So, something can be a Serial but not be broken into Series. Like a long running soap opera that runs for years with no gaps and where the story is continuously developing.
Something can be a Series but not Serial. This could include shows like police procedurals where each episode has common characters but each story is self contained. It can also include non fictional content like a gardening or wildlife documentary show.
Some are both Series and Serial. Like your example of Dallas. You seem confused as to why it doesn't mention "serial" in the Dallas wikipedia page but the term isn't a particularly common label, whereas "series" or "television series" is a much more common and broader term. Series is the more common term as the majority of TV content is broken into groups like this, with exceptions like soap-operas, news and current affairs.