You can determine the files needed for your install by reading the rest of this page for guidance.
There are versions for both i386 (32-bit) and amd64 (64-bit) architectures, this architecture is noted in each of the filenames for download. The amd64 architecture (which works even on Intel 64-bit CPUs) can address more memory and may have other performance advantages, but requires a compatible CPU. If you have a 64-bit capable CPU, use the amd64 version.
The USB memstick includes an installer to install pfSense software to the hard drive on your system. This is the preferred means of running pfSense software. The entire hard drive will be overwritten, dual booting with another OS is not supported.
The USB memstick file is named pfSense-memstick-2.3.1-RELEASE-arch.img.gz. where arch is i386 or amd64, depending on the CPU architecture of your system.
The embedded version is specifically tailored for use with any hardware using flash memory (mostly Compact Flash) rather than a hard drive. Flash memory can only handle a limited number of writes, so the embedded version runs read only from flash, with read/write file systems as RAM disks. The NanoBSD platform has two OS slices and a config slice. One OS slice is used to boot from, the other is used for upgrades, and the config slice is where the configuration resides is held separately.
There are two variations of the NanoBSD platform: The default version which uses a serial console, and another that supports using a VGA console. Each of those variations also comes sized for different sizes of storage media.
The filename for NanoBSD downloads is laid out as follows: pfSense-2.3.1-RELEASE-size-arch-nanobsd.img.gz. In that filename, size can be one of 1g, 2g, or 4g. The arch, as above is for i386 or amd64. The nanobsd part can is either nanobsd for serial console, or nanobsd_vga for the VGA-enabled version.
|pfSense-memstick-2.3.1-RELEASE-arch.img.gz||USB stick installer|
|pfSense-2.3.1-RELEASE-size-arch-nanobsd.img.gz||NanoBSD/embedded (Serial Console)|
|pfSense-2.3.1-RELEASE-size-arch-nanobsd_vga.img.gz||NanoBSD/embedded (VGA Console)|
|pfSense-Full-Update-2.3.1-RELEASE-arch.tgz||Full install update|
|pfSense-2.3.1-RELEASE-size-arch-nanobsd-upgrade.img.gz||NanoBSD/embedded (Serial Console) update|
|pfSense-2.3.1-RELEASE-size-arch-nanobsd_vga-upgrade.img.gz||NanoBSD/embedded (VGA Console) update|
|*.md5||MD5 hash files for download verification|
|*.sha256||SHA256 hash files for download verification|