What happens in C++ when an integer type is cast to a floating point type or vice-versa?

Reinterpreted? The term "reinterpretation" usually refers to raw memory reinterpretation. It is, of course, impossible to meaningfully reinterpret an integer value as a floating-point value (and vice versa) since their physical representations are generally completely different.

When you cast the types, a run-time conversion is being performed (as opposed to reinterpretation). The conversion is normally not just conceptual, it requires an actual run-time effort, because of the difference in physical representation. There are no language-defined relationships between the bit patterns of source and target values. Endianness plays no role in it either.

When you convert an integer value to a floating-point type, the original value is converted exactly if it can be represented exactly by the target type. Otherwise, the value will be changed by the conversion process.

When you convert a floating-point value to integer type, the fractional part is simply discarded (i.e. not the nearest value is taken, but the number is rounded towards zero). If the result does not fit into the target integer type, the behavior is undefined.

Note also, that floating-point to integer conversions (and the reverse) are standard conversions and formally require no explicit cast whatsoever. People might sometimes use an explicit cast to suppress compiler warnings.