IOS51???

what is IOS51?, because every time I use an App, I get a message that tells me if I want to install this

What apps?

wii shop and gecko os.
on the screen of HBC appears IOS36

The Wii Shop is not an app... and I don't see why you'd get that when running Gecko OS...
I think IOS51 has something to do with running the Wii Shop Channel

when I use the wii shop fix(tona),
but I dont know what this is

that installs IOS51 so you can use the Wii Shop Channel without actually updating

so it´s the same that Wii Shop Installer?

No offense, but do you actually know what an IOS is?