It's funny, that's exactly how I started my career. I took the WOMMA certification for Community Management and Community Strategy and at the end of the courses I thought, man those are basically identical and should not be split. You can't do management without having a strategy and in most companies they are one role, because not many can afford to have two people working on Communities yet.
Overall I would make this differentiation:
Strategist thinks ahead in the roadmap for 3/6/12 months and builds networks to support the community manager.
Manager works on day to day community work such as executing engagement, growth and infrastructure and evangelizes the community internally.
But honestly, it could be understood completely differently too.
The one differentiation I have seen work really well before is Community Admin vs. Community Manager, where the admin works on all the platform and infrastructure updates/ roadmaps and the Community manager builds the community to the members through engagement, activation and content.
I like that better, it's easier to define and cleaner to execute. But that's just my $0.02