I must be an outlier. My max hr is max, no matter what. I can reach it running, cycling, shoveling dirt, moving furniture, most any activity (with some caveats). Same with VO2max.
Like the Highlander, there can be only 1 max hr and vo2max value for an organism. How much (or to what percentage) you mobilize, or illicit, those maxes is what the sport dependency shows.
My hr during running and cycling 3 and 10 minute time trials are virtually identical. Thresholds are the same range across sports and activities.