What is the difference between ifne and ifnonnull?

The JVM specification is perhaps clearer on this.

So for ifne (and ifeq etc) the restriction is:

An ifeq instruction is type safe iff one can validly pop a type matching int off the incoming operand stack yielding the outgoing type state NextStackFrame, and the operand of the instruction, Target, is a valid branch target assuming an incoming type state of NextStackFrame.

Whereas for ifnonnull the restriction is:

An ifnonnull instruction is type safe iff one can validly pop a type matching reference off the incoming operand stack yielding the outgoing type state NextStackFrame, and the operand of the instruction, Target, is a valid branch target assuming an incoming type state of NextStackFrame.

Basically ifeq and ifne are for integer values, whereas ifnonnull is for a reference value.

To compare two references for equality, you use if_acmpeq instead. ifnonnull is effectively a special case of that where there's only one operand, because it's always just compared with null.

In terms of how the null reference is represented in data, the JVM specification explicitly allows this to be implementation-specific:

A reference value may also be the special null reference, a reference to no object, which will be denoted here by null. The null reference initially has no run-time type, but may be cast to any type. The default value of a reference type is null.

The Java Virtual Machine specification does not mandate a concrete value encoding null.