The majority of the sound we hear when we take a photo with an SLR, either digital or film, is not from the shutter mechanism. It is from the cycling of the mirror. I strongly suspect that when comparing the sounds of the EOS 77D to the EOS Rebel SL2/200D the difference is in the mirror and the way it is driven, rather than in any difference between the shutter assemblies in the two cameras.
The replacement part number for the 77D shutter assembly is CG2-5514-000. As can be seen below, the springs are fully enclosed in this shutter design.
The replacement part number for the Rebel SL2/200D is CG2-5558-000. The springs are not enclosed in this shutter design.
Spring driven shutters are typically louder than all electronic shutters such as found on higher end models. One would think the actual shutter of the 77D, with fully enclosed springs, would be quieter than the shutter of the Rebel SL2/200D. If one accepts the premise that the 77D is louder than the Rebel SL2/200D¹, the shutters themselves offer no explanation for why the 77D is louder than the Rebel SL2/200D.
In the case of the mirrors and associated springs, motors, etc. Canon does not sell those apart from a complete mirror box assembly that also includes the shutter assembly. From the pictures of the full mirror box assemblies, it is hard to see any details of the mirror and the parts that drive it. The 77d mirror box is on the left, the Rebel SL2/200D mirror box is on the right.
We can look at the comparative specifications for the two cameras for other clues:
- Both cameras have a minimum shutter time of 1/4000 sec. No difference there.
- Both cameras have a maximum flash sync speed of 1/200 sec. Maximum flash sync speed can often indicate a faster or slower movement of the shutter curtains as they transit across the sensor. To get a higher X-sync speed the curtains need to transit the same size sensor in less time. No difference there.
- The 77D has a maximum frame rate in burst mode of approximately 6 fps. The Rebel SL2/200D has a maximum frame rate in burst mode of approximately 5 fps.
- The 77D has a shutter lag of 70ms (as rated by the manufacturer). Canon has not published the shutter lag figure for the Rebel SL2/200D, but the Rebel SL1/100D had an official rating of 75ms. In general, a longer shutter lag allows for a slower mirror movement.
- Both cameras offer Single, Continuous L (low speed), Continuous H (high speed), and Self-Timer (2sec + remote, 10sec + remote) Drive Modes. The Rebel SL2/200D also offers 'Silent Single shooting' and 'Silent continuous shooting' Drive Modes. In 'Silent continuous shooting' Drive Mode the maximum burst rate is reduced to 2.5fps (and the shutter lag time is increased) as the mirror movement is slowed to reduce the loudness of the mirror movement.²
Since the shutter transit times, as indicated by both camera's X-sync speed of 1/200 sec., are the same, the difference between the 77D's 6 fps and the Rebel SL2/200D's 5 fps is in the speed at which the mirror is cycled. A faster mirror probably also includes a more robust assembly to allow it to absorb the higher inertial forces involved with a faster mirror. This accounts for most, if not all, of the difference in sound between the two cameras.
In addition to the slower 'Silent shooting' Drive Modes offered by the Rebel SL2/200D, either camera can be used more quietly by shooting in Live View mode which keeps the mirror locked up during and between shots.
¹ I'm not sure I agree that the 77D is louder than the Rebel SL2/200D. When listening to the single frame recordings at The-Digital-Picture it seems the 77D is just a slight bit softer to me. The faster burst rate of the 77D may make our perception of it louder than the slower frame rate of the Rebel SL2/200D. If both audio files are downloaded, opened in a sound editor (I used Audacity), and expanded to show the actual waveform, one can see that the 77D does have a very brief (2ms) 'click' that is higher in amplitude than the peak of the Rebel SL2/200D waveform. But the later has a much longer (approx. 175ms) sustained "fat" waveform compared to the 77D's shorter (75ms) "fat" part of the waveform.
² In the 'specifications' listing at The-Digital-Picture, they indicate that the 77D but not the Rebel SL2/200D has 'Silent Single shooting' and 'Silent Continuous shooting' Drive Modes. In the body of the respective reviews, the opposite is indicated: they mention the 'silent shooting modes' for the Rebel SL2/200D but not for the 77D. There is no mention of 'silent shooting modes' anywhere in the EOS 77D Instruction Manual. 'Silent shooting modes' are discussed in detail in the Rebel SL2/200D Instruction Manual.