It seems to me that the first season  of most TV shows is a lot (maybe drastically) different than the rest of the show.   Let's look at some shows and their differences in season 1.

Boy Meets World -- Minkus, Topanga with crimpy/curly hair into nature and just weird, Shawn has a sister, Topanga has a sister, only season in elementary school

Sabrina the Teenage Witch -- No Mr. Kraft, Mr. Pool instead of Mrs. Quick, Jenny instead of Valerie, the way Sabrina uses her magic (and not just because she's new at it)

Full House -- Jesse's last name is Cochran not Katsopolis, no Becky, Danny does sports, Jesse kills bugs, Jesse has a mullet (whether he wants to admit it or not)

Of course, there are more shows, but these are the three I can think of most vividly.
Why does this take place?  My guess is that season 1 is the starting point for tv shows and as the show grows the writers think of what they'd really rather do with the characters.  John Stamos wanted to reflect his Greek past on his character so Jesse Cochran became Jesse Katsopolis.  Lee Norris was on a show prior to Boy Meets World and the show got picked up for another season after he filmed the first season of Boy Meets World, so Minkus dropped off the face of the earth.  Most of the time, characters are created first and then the actors are found.  Season 1 is written and filmed.  The actors want to put themselves into the characters, so the characters pick up some of the personality of the actors, like Jesse being a musician. 
Season 1 of Friends was all about Rachel reconnecting with her high school best friend and becoming independent from her father.  They could only continue with that for so long before they needed to find a new angle with her character.  She got a job at Central Perk as a waitress.  She did her laundry on her own for the first time.  The writers couldn't keep hammering on independence, because she basically had it with a job and an apartment.  She can only do everything for the first time only once.  So, they went the angle, which I assumed was their purpose all along, of Ross and Rachel.
A lot of season ones are about changes, giving a reason as to why we're starting the story at this point in time.  The change takes place in season 1 so we cannot keep harping on it in season 2. It gets old at that point.  The characters have changed and now it's about how they are after adapting to the change.  Gilmore Girls season 1 starts off with Lorelai sending her daughter, Rory, to a private school.  The whole season is about how Rory adapts to private school and how her school adapts to her.  The next year of school, she's not going to be trying to adapt any longer.  So, that angle changes. 
Many shows happen to deal with kids in school, whether that is part of the main plot or not.  Each of year of school new kids come in and some old students leave.  This does have an impact on the shows.  It's possibly one reason why season 1 can be so different than the rest of the seasons.  The writers don't say they need have to students leave.  It's just a way for them to bring in new characters and take out ones they don't want anymore.
Another reason that season 1 can be so different from the rest of the show is how the audience responds to certain things.   The audience may hate a character, so they drop him.  Or they may hate a plotline, so they change it.  Or the show is not doing too well in ratings, so they refurbish the show to see if season 2 will be much better.  Some cases, I have found, the show changes stations after season 1 and the new stations wants things their way.
One of the most drastic changes that I can remember is with the show Hogan's Family which was originally called Valerie, named after the actress, Valerie Harper, playing the main character.  At the end of season 1, they decided to fire Valerie.  Valerie is the mother.  You can't just drop the mother.  But, they did.  They brought in Sandy Duncan. I think she played the part of the aunt, I don't remember too well.  So, the show changed a lot.  The show could no longer be called Valerie since it was no longer about Valerie.  It became Hogan's Family and focused on the new character played by Sandy Duncan and the remaining members of the Hogan Family.

I don't know how to end this since I did not intend to write an essay on this topic. I just wanted to discuss it, since it is something that I have been thinking about lately.  I do a lot of thinking. I'm just a thinking person.  So, I'll end it here.