Mindfulness and meditation can be used interchangably. Because you use your awareness when meditating and developing concentration.
Here's some tips, I recommend finding a good teacher though, even if it is just through youtube or a book or something. For example 'mindfulness in plain english' is a good book.
1. Do a sitting practice every day for a fixed time e.g. 30 minutes or something, better to do it twice a day
2. Don't worry about making 'progress' just keeping coming back to observing, and the results will manifest
3. See if you can bring the attitude of observing sensation, thoughts, to every day activities, like washing up etc
4. Try to stay with an object, like the breath, or if not sitting, then sensation of feet touching ground or some part of the body, the body is good to come back to
It's difficult because the mind is used to wandering off all the time, if you keep gently bringing it back, it does get easier because you are retraining it. Like anything worthwhile in life it does take time, patience, and effort. And yeah it isn't suited to some people for various reasons.
Troubleshooting
So if when you sit down to meditate your breath is short and you feel your developing anxiety around it, you can do the following.
1. Lengthen the breath by using mental counting, so I used to count, 1 to 9 as you are inhaling, then 9 to 1 as you are exhaling
2. Then since this is a very long breath, after a while, drop down to counting 1 to 6 on the inhale then 6 to 1 on the exhale, this is a long breath
3. When you are ready, stop the mental counting, and just observe the sensation of the natural breath
These steps can really help calm things down to allow better meditation. When your breathing is long you feel calmer I find.
Another option is using a mantra instead to focus the mind, it is just a word you repeat in your head. Same as the breath, if your mind wanders away from the word, just gently notice and bring it back. Then you can go back to the breath after a while.