Is the gas in your TG oxidizing enough? Is it easily-accessing air? The factor of time can be acting here too. The heating in muffle-furnace is longer. Such difference may indicate incompletion of the particular TG process. You can test this hypothesis by a series of TG runs with various heating rates and various sample sizes. Also, I would make a long TG run with a final cooling segment until the sample cools down to room temperature, and would use that final weight value, since the buoyancy force is reduced (the weight erroneously increased) at higher temperatures.
The maximum temperature have you reached ? check for complete oxidation. Whether you have been raised the temperature to burn it completely. In such cases the ash content may virtually high.
Without knowing all your conditions or the product a couple of points to check,.
I assume that the end temperature is the same for both tests.
Is the TGA trace parallel to the base line significanlty before the end temperature so that decomposition is complete (Ash contents in a furnace is normally carried out until constant weight for 2 weighings).
The TGA work is being carried out in flowing air (to remove compounds from the environment)
Does the material burn in the muffle furnace, is there any loss of particulate material at this point?