neighbour cat problem

my kitty went outside today (she has all her shots and she has been
indoor only) and she's been sort of making friends with this other
kitty i've seen around and thought was living with my downstairs
neighbours. it appears that she she is not with them and we don't
know where she came from. they followed one another around, but only
came as far as 2 feet close, or one of them would start hissing.
Shaina ran inside a few times and the other one followed her into our
apartment like it was her own.

i kept an eye on them to make sure Shaina doesn't run away and
eventually got tired of this, so i tried to get her to go home. she
was hissing at me and attacking me pretty aggressively. she NEVER
does this at home, but i understand she was in a stressful situation.
they really were trying to make friends, in a cat way, so Shaina
wasn't all that interested in going home.

at some point, they got into someone else's patio and it took forever
to get them out. i brought out a can of cat food and the other kitty
was all too happy to eat, while Shaina kept hissing at me. the other
one got much friendlier and cuddlier after she ate. i tried to pick
pick up Shaina to carry her home, but eventually ended up with a bunch
of scratches. finally, i shooed her back home and the other kitty ran
in also. she found Shaina's scratching circle with catnip and went
crazy with it. Shaina looked stunned. i have to go to sleep soon and
i have no idea whom that cat belongs to, or if she has all her shots
and i know i can't leave her here with Shaina tomorrow while i am at
work, so i made her leave. she didn't want to and sat on the stairs
for a while.

now she is outside, but the stairs and looks pretty content. i don't
know what to do with her. should i take her to the vet if i see her
tomorrow and maybe keep her? i'll post pictures of her in the laundry
room and see if anyone calls about her. i just want to know if she
has a human to take care of her. Shaina just finished eating and she
is now looking for the kitty. i really want to her to have a friend,
but i am not sure this is a good idea. any advice?

well, she is gone now. Shaina has seen her before and they sort of
met, so since then she's been trying to run outside, but she gets very
mean when she is out, if i try to get her to go back.

Does Shaina have a chip or ID collar? Maybe you can let her stay out
and come home on her own.

I put a collar on my pussy after neighbors told me that she would zip
in their houses when they opened their doors.

So far she's always come home but couple times she skipped a day.
Don't know if she spend the night in someone house or if she just
wanted to stay out.