Portishead's original station was opened in 1867, half a mile beyond the town which, I note, was described as a "village" in those days. The line was extended to a pier station in 1870, though that was shortlived as a passenger station. On 4th January 1954, a new station was opened 400 yards short of the old station bringing it closer to the Town Centre, but that only lasted just over 10 years as a passenger station - to 7th September 1964.
I think that gives a misleading impression of the geography. So does Wikipedia's piece about the town, making it sound like a fishing village clustered around the port when the railway arrived.
The current port and railway were built as one project, and away from the village at the time. While there may have been a bit of mud to pull little boats onto, there was never a proper port before, and this was basically a farming community. By the time it expanded into a town, there was a barrier of railway and industry that stopped it getting close to the port until this was all closed down starting in the 1960s.
The railway served the port, its station was at the town end - hardly beyond the town, more off to one side. The pier station seems never to have had a regular service; I suspect it was to serve passenger ships which were never that regular (and packets if they ever used the port). And the new station was only built because the old one had to close to make way for the power station, in part using land vacated by the "other railway".