Different muscles for running and as I found out the hard way, for skating too.
Bunch of us guys at work decided to all chip in to buy some ice time at a local arena to play a game of hockey. All older and former players we were all excited to get back on the ice.
Most of the guys were winded after the 20 minute warm up, but not me. I had aerobic capacity from all my riding.
We played for the next hour or so and I was skating as fast as I was when I started but the next day, I felt like I'd been hit by a truck.
Took a while to recover, and despite everyone having a good time and loving being back on the ice again, no one ever mentioned renting some ice time again.