Marketing is a stand alone marketing method or system such as your website, banner ads, autoresponder, blog, online newspaper, online or offline advertising etc.
Marketing Strategy is using those individual marketing tools above (and others) together as your strategy to target a specific market, group of people or audience and in some cases using your marketing tools to study what your competition is doing to see if what they're doing will fit into (and benefit) your individual marketing strategy.
An example of how to tie the two definitions above is to give you a real life example... Long ago my Mom was a true blue hard core Avon lady and was one of the top ones in our city. Besides remembering how I loved to play with all those mini lipsticks and other cool samples as a little girl, I also remember going with her when she made her order deliveries. As we went along, my Mom gave me the job of looking for cars in drive ways or carports and if I saw one it was my job to jump out (watching for other cars of course) and hanging a small bag on their door knob. Inside the bag was some Avon samples and the biggie... a catalog with my Moms name, address and phone number stamped on the back. Her idea (and it worked) was that in the middle of the day if there was a car in the driveway, then it was likely the car of "the wife" since the husband was probably at work. I'm sure we gave away a few hundred free lipstick samples and catalogs to unemployed men stuck in the house, however the other 98%... yep, I'm sure the wives were home.
Sometimes she would have the local printer make her color postcards (4 to a 8.5 x 11 sheet) out of card stock, then cut them at the kitchen table with her paper cutter. Whenever she went shopping, she'd leave a half dozen of these cards in the areas where she knew women would go... feminine products, perfume, dresses etc. and this while shopping for "our" groceries. Lastly, she would offer her current customers $20 in free products if these customers and friends each brought 4 people to her Avon parties at the house (she knew she'd make it back with just a few sales).
In this case my Mom's marketing was a small bag with samples, postcards and a sort of bribe or a nicer word "commission" for her friends that invited 4 to the Avon party. Her marketing strategy was to focus on a highly targeted market of women using her "marketing tools" while looking for other marketing opportunities (thinking outside the box) that her competition was not using. In this case a newspaper ad saying she sold Avon and to call her would not work as well, and putting a pile of samples and catalogs on a table outside of K-Mart (before Walmart was the biggie) wouldn't work very well either. Most of the other Avon ladies focused on parties and word of mouth... My Mom, she was an innovator for sure and it worked.
So for Mom, marketing was the tools that "she chose to use" which she knew would benefit her business the most. Her marketing strategy was to use "her" marketing tools to reach a specific audience of buyers spending as little money as possible in the process.
I hope the example story using my Mom wasn't too long and I hope it helped understand the two terms better. Have a great day there!