Some second order thinking might involve long term thinking but my understanding of what is commonly meant is:

Long term thinking is termporally based, what will X look like in Y amounts of time

Second (or third) order thinking, is based on response to consequences or changes. Could be over a long term, or over a short term.

This seems pretty straightforward but you seem to take issue with it. I'm curious what you think is being messed up by people using these definitions?