What is the difference between BPF and eBPF?

BPF is sometimes used to refer to eBPF (created in 2014) and sometimes to cBPF (its predecessor from 1991). As Qeole noted, you can find a detailed comparison of the two in the kernel documentation.

cBPF (classic BPF) is a small bytecode with two 32-bit registers to perform basic filtering on packets and syscalls. No state can be persisted between two calls to a cBPF program.

cBPF is still used by e.g. seccomp and tcpdump, but is actually translated to eBPF bytecode in the recent kernels.

eBPF (extended BPF) is a new bytecode with significant extensions. The bytecode has a more "modern" form, with 10 64-bit registers, fall-through jumps, and a stack space, enabling easier JIT-compilation to native instruction sets. It can call special functions, called helpers, to interact with the kernel. It can save state to maps using those helpers. It comes with a new syscall, bpf(2), to manipulate BPF objects (e.g., maps, programs, etc.). A good introduction to the eBPF ecosystem is available at ebpf.io.

eBPF programs can be written in C and compiled to the bytecode using LLVM/Clang. The examples in the kernel sources are eBPF programs.