In general the users would display X-axis in temperature by DSC/TGA. The thermal properties of a compound were characterised by the thermal events that linked to the temperature. The time is largely subject to the scan rate, sample Wt and equipment model, etc..

From my experiences, without prior details about the two samples, I can conclude:

1st sample: a) not in a pure phase/form, physically and/or chemically, and not dried properly; b) it converted to a pure phase/form after impurities/wet was removed by heat up to 40min; c) this new phase/form degraded during/post melt at ~65min.

2nd sample: a) in an anhydrous phase/form, b) degraded/melt(?) started at about 60min. The huge endothermal peak can be due to degradation, not melt. The first small peak is probably associated with degradation that started earlier than this huge peak. To be certain it is a melt, multiple experiments are needed. If this peak is consistent and repeatably detected at the same temperature (NOT the time!) at the same scan rate, it will be a melt of your compound. If it varies then it is due to degradation. Actually, there is probably no point to define this peak as a melt or not, as it already started degradation.

I would also suggest you to perform DSC/TGA at 50oC/min to see the difference. Generally, degradation takes longer time than melt.

BTW, it is fairly common that some compounds start melt/degradation at more or less the same temperature.

They could also melt and decompose at the same time, or during melting they could release some entrapped molecules..it depends. You write that from XRD there was a change in the structure, can you determine and attribute the peaks in the pattern to a specific phase? In this way it could be more simple to also explain the thermal data