Sectional gutters come in 10 or 20 foot pieces from the home store, joined with connectors and sealant. Seamless gutters are formed on site from a continuous coil of aluminum, so each wall gets one piece from corner to corner.
The difference shows up at the joints. Sealant breaks down in summer heat and winter cold, and once a joint opens, it drips onto the fascia right behind it. A long sectional run can have five or six joints; a seamless run has none between the corners.
Seamless gutters also tend to be hung better, because the installer is measuring each run on site anyway. That's the moment to set the pitch properly, size the downspouts to the roof, and replace any soft fascia before the new metal goes up.
Sectional gutters still make sense for a short shed or a quick patch. For the main house, seamless is the better long-term buy, especially in a climate that sees heavy afternoon storms most of the summer.