Ironically, what you're doing is called "equivocating." It's the assumption that two different concepts mean the same thing, often because they are named with the same word.

In this case, you are equivocating the concept of judging the relative merits of two things with the concept of noting differences between two disparate things. Both concepts are called "comparing" but they are different concepts.

To use your example, you can compare bikes and cars by speed, by price, by cargo capacity, by viability as a means of transport, by weight, etc. You are looking at the qualities, quantifiable or otherwise, to evaluate the two things in relation to each other.

You can also compare the mechanics of the two machines. A car has an engine and a transmission, a gas tank, power steering and brakes, electronics, a radio, rearview camera, tire pressure sensors, and cup holders. A bike has gears, a chain, pedals, a frame, brakes, a bottom bracket, a fork, shifters, reflectors, and a little cage for a water bottle. These might be similar in components and functionality, but you wouldn't say one is better or worse, because they are each built for a specific function. If you compare a cup holder to a water bottle cage, you could define how they are similar and how they are dissimilar, but it would not be the same sort of comparison as comparing the top speed of a car to the top speed of a bike.

Both uses of the term "compare" are correct. There's no inaccuracies in your language, because the word "compare" means something different in each context. English is full of words like this, where the meaning can be slightly changed or even entirely opposite depending on when and how it is said. That doesn't mean you are using the words wrong. Your confusion of the two concepts is the mistake, not the use of one word to describe two different things.