As I understand it, Rust's beta channel is always one version ahead of stable, and nightly is always one version ahead of beta. However, for some reason, beta and nightly appear to both be 1.16 right now.
If I run rustup update, I see
stable-x86_64-unknown-linux-gnu unchanged - rustc 1.14.0 (e8a012324 2016-12-16)
beta-x86_64-unknown-linux-gnu unchanged - rustc 1.16.0-beta.1 (5276ba72e 2017-01-31)
nightly-x86_64-unknown-linux-gnu unchanged - rustc 1.16.0-nightly (df8debf6d 2017-01-25)
Why isn't beta on 1.15?
Rust 1.15.0 will be released today, 2017-02-02. Apparently the beta channel has already been bumped to 1.16.0 and nightly will follow soon. Read about Rust 1.15 prerelease testing for more information about the 1.15.0 release.