Is it possible in Drupal 7 to create instances of the same block, but with different markup?

Question

CMS

Good time everyone.
Interested in the question of the possibilities of Drupal regarding themization. I read a lot about this topic, and in general I can themize almost everything, but I never found an answer to one question anywhere.
Let's take Joomla for example. She has a great ability to create alternative layouts for modules, and one module can have completely different markup, any. In Drupal, I did not find this, and all such questions and discussions that I found usually ended with the sentences "well, mark it up as you need, and adjust the appearance through css, that's business." But the point is different...
Is it possible, at least in principle, to force Drupal to display two identical blocks, but in different places, with different layout inside the blocks? For example, on the side so that the menu looks like

<li>...</li>
<li>...</li>

and below like this:

<div class="col">
   <a>...</a>
   <a>...</a>
</div>
<div class="col">

If so, how can this be implemented?..
Thank you for your attention.

Answer 1

https://www.drupal.org/project/views