Physiologically & physically speaking:
Strength is the maximal force generating ability of a muscle or group of muscles.
By definition it occurs at zero velocity. However, practically speaking and in the context of the primary muscles involved in cycling, we can define strength as the maximal mass lifted in a one rep free standing squat.
Power is the rate of doing work, or of energy transfer.
It can be also defined as a force x velocity
Power can refer to very rapid acceleration activities taking only fractions of a second or a few seconds (e.g. throwing, sprinting) or to much longer duration activities (e.g. endurance cycling, running, swimming).
For a start, force and power are not the same thing. You can apply a huge force to something (e.g. push hard against a brick wall) but unless it is also moving, then you are applying no power.
Also by definition, the greater the rate at which we do something, the lower the force we are able to apply. Even in maximal sprint efforts on a bike, there is a linear relationship between maximal force applied to the pedals and the rate at which we are pedaling.
Typically, the forces involved in endurance cycling are sub-maximal, significantly so.
e.g. even at 300 watts, at regular cadences and crank lengths, the average effective pedal force is less than 20kg, which means that regular cycling (a vast majority of which is performed < 300W) requires forces roughly an order of magnitude less than (i.e. 1/10th of) our strength.
What matters is being able to apply such low forces repeatedly for long periods and our limiting factor for that is not our maximal force generation ability but rather the biochemical processes going on in our muscle cells, i.e. our aerobic metabolism (ability to turnover ATP).
Increasing strength (i.e. maximal force generation ability) has not been conclusively shown to result in ability to increase our sustainable power, which isn't all that surprising since the physiological adaptations resulting from training that increases strength (e.g. enhancing neurological recruitment, but more importantly, increasing muscle fibre cross sectional area via hypertrophy and associated mitochondral dilution) run counter to those that improve our ability to turnover ATP (i.e. increased mitochondral density and capillarisation inside the muscles, reducing the cell diffusion distance and so on).
The density of mitochondria (which are the energy plants inside our muscle cells) and the ability to readily exchange gases (O2 & CO2) and key metabolites (e.g. glycogen) is the primary limiting factor in endurance cycling.
Fewer mitochondria per kg of muscle mass = lower sustainable power to mass.
To increase strength (beyond an initial neurological improvement which occurs in the first few weeks of such training) requires hypertrophy, which in turns reduces our power to mass ratio.
Now if one is talking about training (with weights for example) that doesn't increase strength, then that's not strength training, and it's a different discussion. [QUOTE/]
