As you say, it varies quite a lot, but likely responsibilities within scope will be:
Manage the technical team of whatever sort you have - may be split QC/QA/Regulatory etc, possibly each with their own managers and supervisors.
HACCP/TACCP/VACCP team leader
Audit lead for customers, suppliers, certification etc - need to know the relevant standards better than anyone else on site
More "upward" reporting as part of senior management team (depending on specific structure) etc.
Likely to require management of departmental budget.
Potentially broader than "just" the food safety/quality management system in terms of regulatory remit, including primary liaison with regulatory bodies - effectively the site expert on food regulations. Depending on scale you may also be expected to represent the business at industry bodies/associations.
May include oversight of other function areas, as for example I've seen businesses put product development under the TM.
Probably responsible for customer-facing technical support across specs, questionnaires, general product knowledge and advice etc, although with any luck you will at least have some sort of team to help you out with that.
Some companies will throw in ethical, environmental, CSR elements (or indeed a range of things that look like they might require a system/policy and no-one else seems to want to take ownership of).
Generally being the person behind the desk at which things of the form "this is a really big problem and we don't know what to do about it" seem to end up
A lot of it depends on scale and character of the business, so somewhere smaller you're likely to still be very hands-on with things like internal auditing, hygiene monitoring, daily QA stuff, but that becomes less significant in larger places - you'll still be responsible for it, but likely that other people will often be doing the physical bits of it on your behalf.
There will be loads of other things that aren't coming to mind right now. I've only been a TM for somewhere in excess of a decade, so still learning the ropes
In general I think it's worth noting that any company worth working for will understand that you're making a step up from a QM role, and they should therefore be interested in your capability rather than expecting you to know everything from the outset. No-one knows everything at the start, or indeed the middle or end. I still learn things regularly, and would be bored as hell if I didn't!
I think it can only be a good thing to ask your prospective new employer for a bit of an outline of the role - it's entirely reasonable for you to need to see this to decide if you want to go for it, even if you ignore questions about experience etc. Honestly I'd be a bit worried about hiring someone who *didn't* want to know what the role was actually about.
In any case, good luck with it if it turns out to be something you want to go for
(there is a private message system if you want to discuss anything about it that you don't want to post publicly)