Terra launched two years before Aqua, so the Terra record starts earlier, with observations beginning in 2000.
Due to Band 6 detector failures on Aqua shortly after launch, Version 5 and earlier snow products from MODIS Aqua were produced differently than their Terra counterparts. This made comparing the output from the two collections harder. In 2012, researchers resolved this problem by developing a post processing technique to restore Aqua Band 6 data to scientific quality. This technique was incorporated into NSIDC products starting in 2015, with the publication of Version 6. Detailed information is available from the MODIS data versions page.
Terra crosses the equator from north to south at roughly 10:30 a.m. local time. Aqua crosses the equator from south to north at roughly 1:30 p.m. local time.
More detail on data capture is provided in MODIS technical references and in user guides for each product.
I had a similar question but regarding the Chlorophyll a product. In the past we always used Aqua MODIS because I understood that Terra MODIS Chlorophyll a had some problems and that more calibration and validation was required. Has this issue been solved and is Chla from both these sensors now comparable? Thanks!