The first image shows a component that was smoking until it burned and changed its shape as shown.
The second image shows another component that looks exactly the same. It exists on a different part on the same PCB.
They have no part number printed on them. They are shorted, I mean they make a buzzer sound during continuity test with multimeter (both the good one and the damaged one). What are they? Thank you,

 

They are shorted, I mean they make a buzzer sound during continuity test with multimeter (both the good one and the damaged one). What are they?

It looks like a low value resistor to me. So, showing a "short" on a continuity tester isn't surprising.

 

They look like surface mount high wattage resistors.
The buzzing sound on continuity test indicates that you are measuring a low resistance. This could be normal.
Often times, an over heated resistor will still survive and indicate the correct nominal resistance value.

In a power supply circuit, it could be used as a current sense resistor.