In one of the Ars Technica articles a saw a table that was comparing the Mx chips, but it was missing some details, so I extended is well I was able with the available information (hopefully the data is correct).
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I made some of the more important distinctions bold. Some of these changes have already been mentioned here, but I guess it doesn't hurt to have them in one place.
M1-3 Basic
The CPU core count is 4P/4E across the board. GPU cores went slightly up from M1 to M2, but the difference here is marginal. RAM size and bandwidth increased to 24GB and 100GB/s.
Given those small changes, I assume that this might actually stay the same for the future, because Apple wants an efficient chip that can be used for the MacBook Air, as well as the iPad Air and Pro. This might also be the reason why Apple is still producing those chips with 8GB of RAM, because 16GB might be overkill for the iPads.
M1-3 Pro
The Mx Pro is a different beast with more performance cores and more GPU cores and a higher memory bandwidth.
I was always perplexed by the 2E cores in the M1 Pro, because I thought that the 4E cores in the M1 made a lot of sense. I guess Apple noticed that too, and adjusted first to 4E and then 6E cores.
What is striking about the M3 Pro, apart from the highest E-core count, is the fact that it is the only chip where the GPU core count went down.
Also the memory bandwidth was reduced from 200GB/s to 150GB/s. Either Apple noticed that 150GB/s is enough or this reduction might be a way to save power.
All in all, I think the M3 Pro is the ideal laptop chip, with the best compromise between performance and power consumption.
M1-3 Max
Prior to the M3 Max, this chip category basically was a Pro with more GPU cores and a doubled memory bandwidth.
Since the M3 Max does not have the 6E cores of the M3 Pro, it no longer seems to be derived from the Pro chip now.
EDIT: I forgot to mention: While the previous Max always had the maximum CPU core count of the Pro, the M3 Max seems to be the first with binning of the CPU cores.
The M3 Max seems to be the best choice for a none portable computer if you don't have the need for a monster like the Ultra.
M1-3 Ultra
I believe Yoused first mentioned that the M3 Max no longer shows the interconnector that was used to combine two Max chips to one Ultra chip. This most likely means that the M3 Ultra will be a completely new design.