a real world point of view
A serial is a story told in a series of consecutively available parts in which the passage of narrative time is likewise continuous. Each episode or chapter typically ends in a cliffhanger to encourage viewers to return the next week to see how the heroes extricate themselves from the previous week's danger. Serials arose in newspaper and magazine publications. The format was transferred to the movies and later to radio and television.
The 1963 version of Doctor Who was produced exclusively in a serial format, each serial having between two and fourteen episodes. Each season had between four and nine serials. Except for the majority of the William Hartnell era, the title of each episode was merely the name of the overall serial, with the episode number appended. Thus, during this era of Doctor Who, the terms "serial" and "story" were synonymous.
The serial format has been largely abandoned by the BBC Wales version of the program, although some serials, like Dreamland, The Infinite Quest and The End of Time have been produced. Other multi-part stories have been produced, but the production team have been reluctant to return to a numerical naming convention. Likewise, several second parts of stories haven't been set immediately after their first parts, thereby breaking the convention of serial storytelling. The term "serial" is therefore rarely used to describe anything produced by BBC Wales. In current parlance, "episode" is usually synonymous with "story" and multi-part stories are called "two-parters", "three-parters" and so forth.