Tiger tanks were extremely rare. So, the chances of a Sherman actually meeting a Tiger were very slim. Only about 1500 Tiger I tanks were made. A large part was used on the Eastern Front. Probably not more than 500 Tigers would ever be in Western Europe and most likely even fewer. In comparison, some 50.000 Shermans were made. So there's at least 100 times as many Shermans than there are Tigers on the Western front. So the odds of seeing and/or engaging one had to be quite slim.
Then add to that the tactical considerations of the Germans and the American Sherman tanks were even less likely to engage Tigers.
The first Tigers were used in Tunesia and those were all knocked out by British forces. The British forces at that time were considered by the Germans to be more dangerous, as they were highly experienced, and thus the Tigers were used against them.
Two Tiger battalions were sent to Normandy. Both were again used against the British forces. In this case, because the northern region, where the British army was deployed, was relatively open, and thus suitable for tank warfare. The southern region, where the Americans were deployed, had the bocage landscape, (pastureland divided into small hedged fields interspersed with groves of trees) which was a natural barrier against tanks. It could be defended very efficiently with infantry armed with panzerfaust, with anti-tank guns, and by tank destroyers. Only a small part of the German tank force was used there, and no Tiger tanks were employed.
After the breakout of Normandy, the German tank forces got trapped in Falaize, and were destroyed by artillery and air bombardment. No Tigers left in the West, until the Tiger II appears in the Battle of the Bulge. And those mostly got stuck on the small roads in the valleys of the Ardennes. Very few ever had a chance to get into battle.
As a result, American Shermans would hardly ever have engaged Tiger tanks. There are only 4 confirmed engagements of the US Army with Tigers. (Of course, it is difficult to confirm everything, so there were certainly were more than four engagements… but it does give an indication of how rare they were.) And this is entirely consistent with the usage of the Tigers by the Germans. The few there were, were used against the British. The handful of Tiger IIs in the Ardennes, were used against the Americans, but they hardly saw any combat at all due to the terrain and lack of fuel.
So considering all those stories of American tankers engaging Tigers and the actual rarity of the Tigers, it is almost certainly a PzKpfw-IV that was actually engaged by the Shermans. The Tiger and PzKpfw IV look very similar from the front. It's just like all the anecdotal tales about '88mm guns, almost certainly they were Pak40 75mm guns.
The British Shermans certainly did engage a few Tigers. Luckily, they had the Sherman Firefly conversion, so they also had the ability to kill Tigers quite efficiently.
I meant to touch on this a while back, as there seems to be a little bit of confusion.
There were Tigers in France after the invasion, one such Tiger was the one belonging to the Imperial Japanese, but was commandeered by Schwere SS-Panzerabteilung 101, it's fate is unknown.
There was certainly a wide range of German AFVs, such as StuGs, PzKfw Mk.IVs and armored cars. For heavy German armor: Panthers, Tiger Is and Tiger IIs were involved.
A short list here:
Schwere Panzerjager Abteilung 653, 1st company/3rd Company: Jagdtiger.
Schwere Panzer Abteilung 301: Tiger I
Schwere Panzer Abteilung 506: Tiger II
Panzer Lehr Division: Panther, PzKfw Mk.IV, Jagdpanzer IV/70
2. Panzer Division: Panther, PzKfw Mk.IV, StuG III
9. Panzer Division: Panther, PzKfw Mk.IV
116. Panzer Division: Panther, PzKfw Mk.IV, Jagdpanzer IV
SS Panzer Brigade 150: StuG, Panther, American, Polish and Russian equipment.
SS Schwere Panzerabteilung 501 (formerly SS-sPzAbt 101): Tiger I, Tiger II
There's more, but this helps to put an end to the idea that there were "no Tigers in the west".
For a great read on the Ardennes and U.S. actions against the Tigers, I'd suggest this:
https://history.army.mil/html/books/022/22-2-1/CMH_Pub_22-2-1.pdf
And I'll toss this pic in...it's a Tiger knocked out near Oberwampach during the Ardennes offensive.