As Andy says VGS(th), i.e. threshold gate-source voltage corresponds to a low current, when the MOSFET barely turns on and Rds is still high.
From a user/shopping perspective what you want to look for is guaranteed (and low) Rds(on) for a given VGS that you plan to use in your application. Alas you did not link to any datasheets or name any specific parts in your question, but I'm pretty sure the guaranteed low Rds(on) is only given at 4-5V for your MOSFET.
Also the MOSFET will not "heat/burn" at higher VGS, as long as you do not exceed the maximum allowed. In fact it's better to drive with a high VGS as possible to ensure it's fully on.
For example, the FDD24AN06LA0_F085 MOSFET has a VGS(th) between 1 and 2V, but the drain current at this point is only guaranteed to be 250µA which is probably far too low to be useful. On the other hand, they promise "rDS(ON) = 20mΩ (Typ.), VGS = 5V, ID = 36A". So you'll normally use this MOSFET with a VGS of 5V or above. Also, for this MOSFET, VGS should not exceed 20V (or go under -20V) or it will get damaged. But anything in this range is okay.
Here are the relevant bits of the datasheet:
Which is detailed as:
Do not exceed ratings:
Also worth noting is the graph of Rds(on) versus Vgs and drain current:
In general, the low Rds(on) promised will have a fairly specialized test condition (like a certain duty cycle). As a rule of thumb, I double it vs. what's promised in the datasheet.