A heart monitor is only one data point or piece of the puzzle when it comes to calculating energy expenditure. Both the elliptical and heart monitor by themselves aren't going to be accurate, at least not in the sense you care about.
Typically, when you want to get a more accurate reading on calories burned, you need a device (fitness wearable, Fitbit, Garmin, etc.) that will accept several data points like: age, gender, weight, height, body fat percentage, etc. With this information along with your heart rate will you paint a more accurate expenditure of energy. Even with this information, it is still an estimate, but certainly better than a heart rate monitor or elliptical on its own.
For perspective think of this: you have two people that are 150 lbs, but one is 5'2" and the other is 6'0". Now put them both on the same exact program in an elliptical or recumbent bike. The net result is both of their calorie expenditures are going to be different. In this case, the 150 lb person at 5'2" will have burned more calories. They're overweight relative to their height and have to work harder to perform the same program as the 6'0" 150lb person.
One more thing to think about is your body adapts and becomes more efficient at performing the same exercises. For example, when you started running for 10 minutes, you might have burned 100 calories. After a month, and performing that same exercise at the same speed, you're now only expending 80 calories over 10 minutes. This can be further exacerbated by your diet if you're in a caloric deficit.
As a side note: if you want to burn fat and sculpt your body, lift weights. You burn more calories lifting weights than you do performing cardio. One exception is HIIT, or high-intensity interval training. It provides a similar effect that strength training provides, EPOC, or excess postexercise oxygen consumption. This is a fancy series of words for something known as the afterburn effect. Which means, you continue to burn calories 12-48 hours after the activity is over.
Why High-Intensity Interval Training Is Best For Weight Loss