You could go further on that point. Jackson's observation was "2 tigers, two panzers...". Obviously Jackson could tell a tiger apart from the other vehicles, but his description of the other vehicles is not entirely accurate as they were Marders, a form of tank destroyer/SPG. Therefore it'd be more accurate to say in this case that everything big was a "Tiger" to an allied soldier, anything else was a "panzer". To be fair to him though the term "panzer" was probably used by all allied soldiers in reference to any German tracked armoured vehicle given that it meant armour.
Generally speaking not even tank crews knew the difference in a hurry. Allied battle reports from Normandy were always reporting Panthers and Tigers engaged and/or destroyed, but when the burnt out wrecks were found they'd often be Panzer IV's or similar. In certain circumstances, due to it's special armour the Panzer IV H/J resembled the Tiger enough to be mistaken for it quite easily.