When you say "free energy" or "a perpetual motion machine" you may mean one of several things:
(i) A machine (eg. solar/wind powered things, plant life, fusion power etc) in a local system (eg. the earth) which run on energy from a source (ie. hydrogen in the sun or on earth) which is effectively infinite with respect to the local system (thanks LSLGuy). Possibly a source no-one knew about before. This IS POSSIBLE and EXISTS.
(ii) A machine which if it lived in perfect isolation could run literally forever, and has zero losses even though it's impossible to extract any energy form it. eg. one rock orbiting another rock in a newtonian universe. (The only problem is to make it complicated enough to call "a machine" rather than "a rock") This is POSSIBLE but DOESN'T ACTUALLY EXIST because anything in the universe even if effectively undisturbed, will EVENTUALLY after enough trillion years be interfered with by minute amounts of interstellar dust, protons and neutrons spontaneously decaying, orbits slooowly emitting gravitational radiation[1], etc.
(iii) A machine which runs in a non-isolated environment (eg. on the earth). This is STATISTICALLY IMPOSSIBLE because the second law of thermodynamics observes that all such things always interfere with the environment, and in doing so increase in entropy, which is normally visible as "sort of running down". This isn't necessarily obvious, but is true, which is why it's important. I say "statistically" impossible because it describes what tends to happen. If you start with a room with two different gases in it at two ends, it will eventually mix until the two gases are equally distributed. But it's always possible (though vanishingly unlikely) that the gases will both suddenly jump to one corner of the room. But you can't DESIGN that to happen.
And so
Sometimes people use the terms confusingly.
If you talk about finding "free energy" sometimes you mean it in sense (i), which is generally a good thing: even if it's not literally free, it fulfils the requirements we want to seek, ie. we can have as much of it as we can get. Other times they mean in sense (iii), which means that they're clearly wrong, even if you can't point out WHY they're wrong.
If you say "perpetual motion is impossible" you mean sense (iii). Someone else may mistakenly think (i) and (ii) are a counterexample, in which case they may be correct you should have spoken more clearly when saying what is impossible, but you are quite correct that you're thinking of something specific which is in fact impossible.
If someone says "isn't XXXX a counterexample to perpetual motion being impossible" they generally have in mind a machine which either (a) draws power from some effectively but not actually infinite resource, often one which may not be apparent (b) is in case (ii) or (c) looks like it ought to go on forever, but actually loses energy to the environment slowly as in case (iii), sometimes in a non-obvious way. Either something like "ok, so the water wheel runs the pump and the pump runs the water wheel" forgetting that the efficiency is much much less than 100%. Or something where the efficiency is much closer to 100% and isn't obvious.
(Or sometimes (iv) complicated quantised physics shenanigans I don't understand. But that's not normally what people are thinking of.)
footnotes
[1] I just thought of gravitational radiation today. I'm sure I didn't include it the last time I had this rant, and would have said that without friction you could have had a system running in isolation for ever. I think you still could CONCEPTUALLY, it just doesn't happen to work in reality.
(i) A machine (eg. solar/wind powered things, plant life, fusion power etc) in a local system (eg. the earth) which run on energy from a source (ie. hydrogen in the sun or on earth) which is effectively infinite with respect to the local system (thanks LSLGuy). Possibly a source no-one knew about before. This IS POSSIBLE and EXISTS.
(ii) A machine which if it lived in perfect isolation could run literally forever, and has zero losses even though it's impossible to extract any energy form it. eg. one rock orbiting another rock in a newtonian universe. (The only problem is to make it complicated enough to call "a machine" rather than "a rock") This is POSSIBLE but DOESN'T ACTUALLY EXIST because anything in the universe even if effectively undisturbed, will EVENTUALLY after enough trillion years be interfered with by minute amounts of interstellar dust, protons and neutrons spontaneously decaying, orbits slooowly emitting gravitational radiation[1], etc.
(iii) A machine which runs in a non-isolated environment (eg. on the earth). This is STATISTICALLY IMPOSSIBLE because the second law of thermodynamics observes that all such things always interfere with the environment, and in doing so increase in entropy, which is normally visible as "sort of running down". This isn't necessarily obvious, but is true, which is why it's important. I say "statistically" impossible because it describes what tends to happen. If you start with a room with two different gases in it at two ends, it will eventually mix until the two gases are equally distributed. But it's always possible (though vanishingly unlikely) that the gases will both suddenly jump to one corner of the room. But you can't DESIGN that to happen.
And so
Sometimes people use the terms confusingly.
If you talk about finding "free energy" sometimes you mean it in sense (i), which is generally a good thing: even if it's not literally free, it fulfils the requirements we want to seek, ie. we can have as much of it as we can get. Other times they mean in sense (iii), which means that they're clearly wrong, even if you can't point out WHY they're wrong.
If you say "perpetual motion is impossible" you mean sense (iii). Someone else may mistakenly think (i) and (ii) are a counterexample, in which case they may be correct you should have spoken more clearly when saying what is impossible, but you are quite correct that you're thinking of something specific which is in fact impossible.
If someone says "isn't XXXX a counterexample to perpetual motion being impossible" they generally have in mind a machine which either (a) draws power from some effectively but not actually infinite resource, often one which may not be apparent (b) is in case (ii) or (c) looks like it ought to go on forever, but actually loses energy to the environment slowly as in case (iii), sometimes in a non-obvious way. Either something like "ok, so the water wheel runs the pump and the pump runs the water wheel" forgetting that the efficiency is much much less than 100%. Or something where the efficiency is much closer to 100% and isn't obvious.
(Or sometimes (iv) complicated quantised physics shenanigans I don't understand. But that's not normally what people are thinking of.)
footnotes
[1] I just thought of gravitational radiation today. I'm sure I didn't include it the last time I had this rant, and would have said that without friction you could have had a system running in isolation for ever. I think you still could CONCEPTUALLY, it just doesn't happen to work in reality.