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.

I see it as more like : these thinga are too dissimilar to be compared meaningfully. Like if some article says which is the best tool? And they give you a rake, a network router, and a nailgun. Then you meed context. You can make a matrix of differences and similarities but depends what you are trying to compare. Comparing could be: All are durable, All save time on tasks, All can break with misuse.
But can also be nailgun and router is bad for raking leaves.

Attributes and values. The more attributes two things have in common, the easier to compare them by value. But when two things have very few attributes in common or the attributes they can be compared on are very broad, general or abstract, it is harder to compare them.

But, two things can have all the exact same attributes but totally different values of each. Thus they're dissimilar or unequal when compared, but can be compared. The cybertruck and a Ford F-150 can be compared but are dissimilar. For all the attributes they share are unequal. A melon and a pogo stick are harder to compare, for their defining attributes hardly overlap except on a very abstract way.

This said, it's all semantic subjectivity. Poetry compares dissimilar things and equates unequal concepts all the time.

They mean they can't be compared in any significant way or they can't be compared except in the broadest terms. Yes I could compare you to a summers day but really only if im waxing poetic.

What they actually mean is rather "these two things are very dissimilar", or "these two things are unequal".

I think what they mean is “This is an invalid comparison”. For instance, the idea that two concepts are “apples and oranges” invokes the idea that apples and orange can’t be compared. But of course they could be compared as fruits (which would you prefer to get in line at the cafeteria? Aren’t you inherently inviting a comparison? I’m with you on that).

However, if one were asking whether golden delicious apples are better than honeycrisp apples and someone butts in that navel oranges are the best, they’d get the same “navel oranges and golden delicious/honeycrisp apples can’t be compared” response because they’ve brought up an invalid comparison in the context of the comparison. Apples and oranges.

I take "cannot be compared" to be a sort of shorthand claim - they aren't actually asserting that the two things literally cannot be compared at all, but that they cannot be compared meaningfully or relevantly.

False dichotomy, because there's never two options, there's all the options, pizza tonight or tacos? There's millions of alternatives.

Alternatively, the statement can be made in either of two additional contexts:

1. I didn’t bother to compare these because of their glaring dissimilarities/ my own laziness.
2. It is obvious to the casual observer that a comparison between these things would not produce a meaningful result, and therefore I’m pointing out that comparisons would be moot.

Apples to oranges. What is similar? They are fruit. That's about it.