Microphone selection and placement have a lot to do with what gets recorded. The room reflections will play a part too, depending on how close miked you are. What kind of mic? How close are you putting the microphone from the speaker? Are you pointing it right at the speaker or off to the side? Using a mic can be a game of inches (or less).
As far as going direct from your amp, it sounds like a gain mismatch. If your amp is sending out a line level signal, but your recorder is expecting an instrument level, you will definitely get the distortion you describe. You need them both the same level. Does your recorder have the option of choosing line or instrument level?
There are a lot of resources of information out there, you may need to do some digging.
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