My childhood best friend went into the Army to be a Ranger. He once told me that there is basically no higher priority event than a search and rescue mission. Down to a man, if you are captured, or at risk of capture, special forces and black hawks get called in with the ability to use any means necessary to get you out of there alive. He said it was an extreme source of pride for him personally to see how far they went to save their men on the ground and that this policy empowered you to fight harder and more confidently knowing that the full force of the US military was behind you (ie "no soldier left behind")
While I am no expert on these things, a few of the videos / articles / images I've seen of Russians fighters in Ukraine lead me to believe they don't feel this similar level of support from their armed forces, which could be contributing adversely to the outcome (from their perspective).