A CTO's perspective
A strategy is a researched, well thought out and planned action plan for achieving your goals and objectives. A capability is having the ability to expertly apply skills in practice in an ethical, professional, safe, and expert way.
Here’s an example:
Let’s say you want to run a marathon and win. You have never done this before. You would not turn up at the start line on the day, say “I am here” and expect to finish the race or win. Rather, to successfully run and win the marathon (your goals) you would sit down long before the race day and research what you need to do to achieve those goals.
You would find out what shoes and clothing is best, how much fluid you will need during the race and where you can find it along the race track. You would train for some time before the race to ensure you have the endurance to run the distance and the strength and speed to win. You would research your competitors to find out what a win would mean - the times and pace you would have to achieve to win on the day.
Here is an example of a strategic capability in business.
Being in business is no different to the marathon example. Each day businesses win/lose clients against competitors. If a business loses too often for an extended period, it will no longer be able to stay in business. We see examples of businesses closing every day. So, to stay ahead of competitors businesses need to research their competition, sector, industry, formulate a solid, effective strategy, and develop the capabilities needed which they may or may not have, to carry out the strategy actions of stay ahead of the competition. Today, in our digital world, businesses strategically use scientific knowledge as a capability for staying ahead of the competition.