Product managers can be either only business oriented or also very technically involved.
When applying for a job you will not know the structure of the team and often you will have a vague understanding of your job responsibilities and the team structure just based of the job description. You will be able to identify whether the position is technical or not based on the expectations. If the job description states computer science is a must, or your product is highly technical, for example, "Building SDKs", or you build a product that serves developers, the product is very heavy on backend work - it's most definitely a technical product manager. Now, that doesn't mean you shouldn't apply because you don't have a computer science degree, you can earn the knowledge through experience. I did just that.
A business product manager deals much more with customers, prioritizes the requests and plows through the politics of the company, leaving all technical complexity to the engineers. There is a high need for business product managers as this role often times entail a sales person, a customer service representative and a little bit of a visionary.
And do not worry. Product management as a profession is pretty new. It allows you to count in any business management experience you've had before and counts towards your new career.