There seems to be some confusion about how sub-domains are treated so I will try and clarify some of this.
Using example.com, www.example.com is a sub-domain of example.com and we take it for granted that these are the same. But they are not. It is very possible, though no-one really ever does this, that example.com and www.example.com are completely different sites with different content and so on. And Google will treat them as such. This also holds true for other-topic.example.com. Both sites will be treated as two completely separate sites with some exception.
The exception is this. Let us make the example clear for a moment. Example.com does a 301 redirect to www.example.com so we can throw away this for our discussion. We will assume that www.example.com and example.com follows tradition and we will greatly simplify the example. Other-topic.example.com and example.com are within the same realm. These are related sites using a semantic database designed to combat web spam and for other reasons of trust and ranking.
While each site will have to perform on it's own, any sub-domain cannot be fully ranked simply because some metrics do not exist for sub-domains. As well, some metrics for the parent domain will effect any sub-domain as a matter of trust. Here is a list off the top of my head.
- Site Age
- Changes in Registration
- Registrant Quality (has the registrant been penalized in the past?)
- Registration Period (generally not a big factor)
- Registrar Quality
- Private Registration Quality
- Parent Domain is Black Listed (or has a moderately significant black list history)
- TLD Quality
- DNS Stability (changes in IP address primarily though far more involved)
- Parent Domain is not known for previous issues- Spam, Phishing, Fraud,
Cloaking, Inciteful, or other Bad Content
- Parent Domain has Company Physical Address, Phone, E-Mail Address and is
- Parent Domain is Child Safe
Because these metrics are missing for sub-domains, the semantic link map ties domains and sub-domains together to pass along at least some portion of these trust metrics to properly rank the sub-domain.
As for content.
The sub-domain will be treated as a separate site in regard to content and indexing. Any sub-domain can be a completely different topic from the parent domain and any other sub-domain. In fact, this is quite normal and sub-domains are often used to segregate/divorce topics from the parent domain as not to dilute/effect the SEO prowess of a parent domain.
In this case, I would not worry too much about users being confused. This is a personal call if you think the two topics would have a negative effect. As far as search engines are concerned, this is not an issue.
Again, each site will have to compete to gain search relevance and SERP performance. However, the performance of the parent domain does influence the SERP performance of the sub-domain through trust metrics gained by the parent at least in part.