DSL vs Cable internet?

DSL vs Cable internet?

So I am not quite sure of the differences. I have read that DSL is fed
into the home via the phone line, and cable is, of course, through the
cable jacks. I currently have a 30Mbps cable connection but am forced to
downgrade to a 6Mbps connection due to the service not being available
where I am moving.
What are the main differences? For example, as I said I have a 30Mbps
connection now that costs $30/mo, but the 6Mbps DSL service I am being
forced into is going to cost $35 (different location and different
company)! I figured the prices would be similar but was surprised that was
not the case. Are there some underlying differences between the two
services that may justify such a difference?
If I have a 6Mbps DSL line, will a 6Mbps cable line be the same speed? I
realize there are circumstances to consider when making this judgement
(i.e. whether you have a dedicated line to your home or a community line),
but assuming the situations are exactly the same are they similar?
Also, why have I seen some internet providers offer packages upwards of
105MBps, while a company like AT&T has 'Extreme' package (or whatever the
fastest may be called) only on the order of 18Mbps? Is cable capable of
speeds that much greater than DSL?