Odd that the Manager picks it up but the BTC wallet one won't... Possibly a weird driver glitch... but that would usually mean that you can't use the Manager either.
Have you tried using the Manager to uninstall all the apps from the device... and then re-add the Bitcoin coin app on the device? Or maybe try and uninstall and reinstall the Ledger Wallet Bitcoin chrome app?
In post number 6 I suggested to him to uninstall apps from Chrome, sometimes new firmware and old apps create problems. The OP seems to have serious problems with basics, as you say it is not possible that Ledger Manager is connecting and Ledger Bitcoin Wallet not...
I use OS not windows,no sounds,was thinking that I need check singed message through ledger bitcoin wallet extension for chrome not the app inside manager...
You use OS ( operating system ), but not Windows - so we need to guess which one you use, maybe MAC or Linux - something else?