According to wikipedia (and as discussed in various places in the Android docs, including here), Android is “based on a modified version of the Linux Kernel along with other open-source software”.
iOS is mostly proprietary software, so there is less publicly available information about the operating system, but according to Wikipedia, it “includes components of the Mach microkernel and FreeBSD” and is a “Unix-like” operating system. Where “Unix-like” in this context is defined in https://www.wikiwand.com/en/articles/Unix-like, and means that the operating system in question:
behaves in a manner similar to a Unix system, although not necessarily conforming to or being certified to any version of the Single UNIX Specification