I recently switched from being a competitive road racer (Cat 2 in NorCal) to competitive running. I never ran previously and was not training seriously until my early 20s.
First off, the training methodology differences are very interesting. Cycling is currently dominated by the watt. Everybody prays at the altar of objective power data. Having heart rate data is nice, too, but merely as a secondary and somewhat subjective metric that helps provide context on the power numbers. RPE is occasionally used for establishing, let's say, a recovery riding zone, but power is really the only objective metric.
Cycling power zones are established by performing a somewhat standardized field test that measures, usually some kind of VO2 capacity (let's say a 5' effort) and then a threshold capacity over the course of a 20' interval. The 20' interval is typically multiplied by 0.95 to find the true power that is the rider's hour-long threshold.
Watts are a temporal unit and are actually one joule per second of energy. So, a ride's energy output can be measures in joules - or, more easily - kilojoules. There is a relationship between kilojoules and calories, so cyclists can somewhat accurately determine their nutritional needs.
Also, kilojoules can be fed into various models to figure out how fit you are on a large scale and how fatigued you are at any point in time. This is someitmes referred to as CTL or chronic training load. It's common to shoot for a particular CTL for a goal race and have a specific fatigue level that is not too high for priority races.
PHEW. Now, running! A lot of RPE! A lot of basing zones on race PBs. A lot of people even set their zones based on heart rate! Which, to me, seems crazy, given that my heart rate will change significantly based on temperature, hydration level, caffeination, and all sorts of other things.
As I get into running (I only have about 300km in my legs so far) I'm slowly getting used to the various training paces. A "tempo" run is very similar to what I would consider a cycling "threshold" effort level, which is extra confusing given that cycling has "tempo" zones too which actually fall distinctly below threshold.
My initial findings are that cycling fitness does indeed translate to an extent as I have experienced rapid adaptation. Earlier this year I ran a 18:30 5k, which obviously is slow, but not terrible for literally a first 5k and with no running training. More recently I just ran a 17:00 5k with about a month of training in my legs and with much more controllable effort. I suspect that these gains will quickly subside but I'm curious if anybody else has transitioned from cycling to running and found similar adaptations.
My main challenge now with coming up with a decent training plan is that my muscles perhaps haven't caught up with my aerobic system, so I have to be very careful of biting off more than I can chew and injure myself. I'm planning on entering some 5k races this year to get started and then play with more distances later.