Reference In SM Anime Ending

PikaFUSION
Sorry for taking so long to answer your question - I was kind of waiting for someone else to give you an answer because I was being lazy. I'm just gonna base this on the translation on bulbapedia:


So, the lines you are wondering about should be these, right? In my opinion, the first three lines should simply be referring to Ash and his bond with his Pokémon with the mention of the different types of pokeballs being less of a metaphor than you might think. You could basically say that it means something along the lines of: Even though I caught you, that doesn't mean that you instantly like me even though I am your trainer. But if we dance together (which I assume simply stands for: if we have fun and work together), we'll get closer and stronger. The fact that Ash dances with Pikachu throughout the first part of the ending sequence supports this.

Now, moving on to the last four lines:
As soon as the singer sings the first line, the imagery in the ending changes to a scene of Ash holding Pikachu up in the air with both of them smiling - so it should be pretty obvious who he is referring to here.
Once the last three lines start, the scene changes to a scene that features Ash and Pikachu running somewhere, with pictures of the Sun & Moon cast flashing by - and that also shows us what those lines are referring to: to the bond between the Sun & Moon cast (including Ash and Pikachu, of course). The SM anime has a very family-like feeling when it comes to the relationships between these characters - the fact that Kukui basically takes the role of Ash's "father" in this season only makes this more obvious - and this is what the song is talking about: that Ash is enjoying his time in Alola with everyone. That he values the memories he has with everyone. That the whole cast supports each other like a family.

The last line
marks the end of the running sequence and Ash and Pikachu reach their destination: the place where the rest of the Alolan cast is waiting for him. This line simply is a promise to meet again in the future, because eventually, they're going to have to part from each other, and to relive all the good memories they shared together.

Also, quick shout-out to that one line in the opening, because I have seen way too many people say that it refers to Serena even though it clearly refers to Lillie:

Now, first of all, the whole theme of the song makes it incredibly clear that it is referring to Ash's journey in Alola, so we pretty much just have to look at which girls deserve a special mention. It is pretty obvious that the entire cast except for one girl is incredibly comfortable around Pokémon, except for Lillie, who has some sort of childhood trauma and can't even touch them. So, with Ash being Ash, his mention of her in the song (I'm referring to the singer as Ash because the opening is sung by his VA) just tells you that he wants to help her get over that, so that he can go on an exciting Pokémon adventure with her, too. It wouldn't make sense for this line to refer to any of his past companions because the song refers to his Alola journey and none of his other companions is even anywhere near him, nor would they need any extra mention (which sounds harsh, but what I mean by it is simply this: the others have no problem with adventure, so he (theoretically) could always go on an adventure with them. Lillie can't do that though because of her fear of Pokémon.). The fact that I've seen some translations, which translate that line as "with the sun, moon, Pokémon and even her" only makes this more obvious.
Also, there are about a million different translations of that line, so take this with a grain of salt - this is the most trustworthy translation I found though.