What Temperature Is Really Medium-Rare for Steak?

Today I cooked the Pan Seared Steak With Black-Pepper-Lime Sauce using flank steak from Copokish and it was delicious. However, in reading the directions it said to "cook until center reaches 120 degrees F (for medium rare). That's the first time I ever saw 120 degrees called medium rare. In a table at Serious Eats has a table for sous vide steaks that says 120-128 F is very Rare to Rare and 129-134 is medium rare. ATK's Sous Vide for Everybody says cook steak to 130 degrees in most cases because that is the point where most bacteria is killed, i.e. the meat is essentially pasturized. I usaully "pan fry" steaks after using my sous vide because they come out perfect everytime. If I'm going to save some for tomorrow I will cook to 130.5 degrees to be sure and it was just fine, still leaving some bloody juice on the platter to mix with the rest of the sauce. I find steak much less than 130 degrees having too soft a texture, sort of like trying to saw rubber.

I understand that if you pan fry it and let it rest for 10 minutes the temperature will rise, but probabably no more than a few degerees on a steak as thin as flank or fltatiron (my favorite). From the makers of Thermapen:

"For example, if you have a particularly thick New York strip and you like your , you would select 130°F (54°C) as your target resting temperature and subtract, say, 4 degrees F (2 degrees C) from that to calculate your pull temperature as 126°F (52°C). This is the number you will be watching for when measuring the thermal center of your steak. When the thermal center hits your calculated pull temperature, it’s time to remove the steak from direct heat."

Does all this matter? Only in respect you are probably not going to end up with the doneness you expected and there could be a slight risk of food safety. However, if you are used to eating medium rare hanburgers you are risk averse.

PS Cookish is one of my favorite cookbooks of yours,