Yes, these two typewriters do have a very similar styling and a similar nice chrome trim. Under the hood the look quite different (My impression by looking at photos from classified ads). I don't own any of them.
I don't think the two manufacturers had any kind of partnership. Olympia was the bigger one - in the late 1950s they had five times more employees than Torpedo. And the Olympia company had more commercial success and lasted longer til the early 1990s in contrast to Torpedo which was defunct by the late 1960s.

-Rainer (Triumph-Adler employee a long time ago)

Red carbon paper is also used for some artworking purposes.
Example: https://imcclains.com/newsletter/?p=254
I don't know but maybe the use as a carbon paper for typewriting purposes was not the primary intended application. But a nice possibility anyway.

I discovered an Olympia SGE D52 in a German classified ad that has a white tab key or white tab bar (how to name it?), but no visible option to set or clear a tab stop. The white key uses the entire usual three tabulator function keys cutout of the typewriter's case without the normally present tab set/clear keys left and right of the tab key. It also does have no inscription like the usual arrow. Does it have any functionality at all?



For comparison here's a usual SGE D52 (different classified ad):



I find that somehow odd. Maybe the white tab key was later redesigned by someone. The key doesn't seem to have the concave surface of a normal tab key, but rather a convex surface, like normally found on a space bar. The key also seems to be the same length as the space bar.

This typewriter also doesn't have a paper feed lever. This is often omitted from cheaper models.

Does someone has more information about this kind of modification?

Let's try to get an answer from Google via it's artificial intelligence chatbot Gemini.

Q:
Do you know the 'Typewriter Talk' internet forum? Why does the Google search for 'typewriter forum' have no direct results for this search phrase in relation to the 'Typewriter Talk' internet forum?

A:
>>> It's true that searching for "typewriter forum" can yield a variety of results, and pinpointing a specific forum like "Typewriter Talk" can sometimes be tricky. Here's a breakdown of why this might occur:

• Search Engine Algorithms:


• Google's algorithms prioritize relevance, popularity, and other factors. General terms like "typewriter forum" might bring up broader results, such as popular Reddit threads (r/typewriters), general typewriter community websites, or large databases.
• Older forums or those with less frequent updates might rank lower in search results.
• Varied Online Presence:
 The "typewriter community" exists in various forms: forums, social media groups, blogs, and email lists. This fragmented presence can make it difficult for a single forum to dominate search results.  
 Some online communities, especially older ones, may not have the same level of SEO (Search Engine Optimization) as newer platforms.

Community Structure:
  "Typewriter Talk," like many niche forums, might rely on word-of-mouth and direct links within the community, rather than heavy reliance on search engine traffic.
  Also some older forums can have older web technology that is not as well indexed by modern search engines.

•  
• General Search Terms:

[*][color=#000066]When a general search term like "typewriter forum" is used, search engines will return the most popular and broadly used websites. So sites like reddit, and sit
…

Eagle wrote:

A technical drawing of the Olivetti Praxis 48 that shows that principle:
 

And I have to correct an error that I've made.
The technical drawing shows a Olympia SGE 50.