Sekt is the German word for sparkling wine. All sparkling wines are first made into wine and then the wine (base wine or cuvee) is fermented again. Sekt or sparkling is made in three different ways:
1) methode champenoise (Champagne methode) which means the the secondary fermentiation happens in the same bottle that it is served in like it does in real champagne (Champagne is sparkling wine from the Champagne region in France, so there is no California champagne, only California sparkling wine)
2) the secondary fermentation happens in a bottle, but for cost savings the bottles are emptied, the sparkling wine filtered and rebottled.
3) charmat methode (bulk production), which means that the second fermentation happens in a tank and the sparkling wine is later filled in bottles (much cheaper and mostly used for lower end sparkling wines)
The big difference between Sekt and Schaumwein is that Schaumwein is only fermented once, produced in bulk / a tank and bottled. Mostly of medicre to low quality, but can be refreshing in the summer.