I assume that you are talking about the break in the DTA or DSC curve that occurs at Tg for an inorganic glass. It isn't really a peak, since this is not a first order transition, but is really a change in the specific heat baseline. There is a "peak" if the sample is not well annealed.

The difference in temperature is due to the fact that you are measuring different properties, i.e. enthalpy vs volume. The sample sizes are different, which results in the actual sample temperature (as opposed to that indicated by the thermocouple) lagging the indicated temperature by different amounts. It is normal to use different heating rates in the two measurements, (maybe 4 K/min for dilatometer vs. 10 or 20 K/min for the DTA/DSC) which also results in a difference in the lag between actual sample temp and that of the indicator thermocouple.

You really need to understand the concept of the glass transformation in inorganic glasses to understand the fine points of this result. It is well documented in the literature.