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Depends.
You got two kinds of distortion, if you look at it theoretically.
Distortion is nothing more than adding harmonics (higher frequencies that have a relationship with the fundamental frequencies. For example, 300, 450, 600 are all harmonics of 150 Hz).
Now you gotta make a difference between odd and even harmonics.
Let's take a simple 1000 Hz example. 2000 Hz, 4000 Hz, 6000 Hz are even harmonics, 3000 Hz, 5000 Hz, 7000 Hz, etc... are odd harmonics.
Take a simple sine wave. The sine wave doesn't have any harmonics, only the fundamental frequency. So, a 1000 Hz sine wave only has 1000 Hz, nothing else. I think you all know how a sine waveform looks (~).
Take a 1000 Hz square wave. Square waves are the extremes. It's the fundamental frequency of 1000 Hz + only odd harmonics (for a perfect square wave, which doesn't exist, the odd harmonics would extend infinitely. As it's impossible to make something like this with the actual technology, the harmonics decrease in amplitude the further you look). Likewise, you all know how the waveform of a squarewave looks (a perfect squarewave would have infinitely steep flanks, and absolutely flat tops and bottoms).
Do you hear the difference between the sine and squarewave? Right, the squarewave sounds very harsh.
That brings us to the first conclusion, adding odd harmonics makes the sound more harsh. Looking at the waveform, it either means making the flanks steeper, or flattening the curves. The more you do this, the more odd harmonics you add, the harsher it sounds, with the extreme case being the square wave. Think digital distortion here...
Now, when you add even harmonics, it sounds much more pleasant (think analog tape/tube distortion here : the so called "warmth" of tubes).
So second conclusion, adding even harmonics : more pleasant sounding than odd harmonics. BUT... How would you translate this in the waverform??? Well, that's basically the symetry of the waveform that changes, and mostly the symetry compared to the X-axis (so in short, if you take that 1000 Hz sine wave, and "transpose" it higher or lower compared to the x-axis, it would mean you add even harmonics). So with a lot of even harmonics, you would eventually get the same figure as with DC offset, taken as a snapshot.
The difference would be that DC offset would be throughout the waveform, as "normal" even harmonics would still return to zero once and a while. But it's rare you get significant DC offset by even harmonics (ie, a lot of distortion).
So, check your distortion settings if possible...
Usually, DC offset problems occur at the recording stage, and are best cured there (get the source right, remember), although in modern software, the detection algorhythms aren't too bad.
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