I see strategy as more 'what are your goals?' and tactics as 'how will you achieve those goals?'.
So strategy might be "we need to collaborate more" and as a result tactical might be 'we need to implement Sharepoint".
I was recently asked to give a presentation to our CEO on what our "IT Strategy" is. I basically refused on the grounds that IT Strategy is really just a response to "Company Strategy" and I wasn't made party to what our company strategy is. I was kind of "you tell me what the company strategy is, or what the business plan is, and I'll tell you how we can use IT to achieve it".
Too often I think IT departments work in isolation to the general business plan. They're off implementing Exchange, or ERP, or Sharepoint without asking 'how does this help meet the short to medium term goals of the company", or "how will this make the company more profitable". So they implement technology based on how the company is currently setup, blind to the fact that companies are dynamic things - they're constantly changing, expanding, retracting, moving into new markets, moving out of old markets. Without the vision, IT is always playing catchup to what the company is trying achieve tomorrow.
So I'd say I leave strategy to the CEO, and I only do tactics. As managers we know what our company looks like today, and we know what are weaknesses and strengths are today, but we have no idea what our company will look like in five years time. Only the CEO has (or should have) that vision of how he sees the company developing.
But what strategy I do do, I probably do it lying in bed at 3am unable to sleep. That's when most of my long term planning takes place, unfortunately. That's when my "vision" seems to be at its most clear.