Turn signals use a flasher relay. When the flasher goes bad, either your signals do not work, or they stay lit without flashing.

The hazard lights also have a flasher relay, but it is independent of the signal flasher.

It's a small part, is easily replaceable, and cheap.

Don't know what model you have, so I can't tell you where to find the flasher on your car, or the cost of the part...

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car