I'm not looking for an exhaustive list of all the small details, but I'm guessing there are a few big changes between 3rd and 4th edition. Can someone give a short list of the biggest changes?
Long time player of ArM5 here, with my recollections:
3rd edition to 4th
The largest differences are those not listed on page 262 of ArM4 Core. The publisher changed from White wolf to Atlas and therefore the fundamental assumptions behind the game changed.
The largest change, in my opinion is that ArM4 has "spell boosting" where you can burn vis for an extremely non-trivial range, duration, or target increase. This changes the balance of power of magi in mythic europe.
In ArM3, due to a desire to be somewhat compatible with other white wolf products, there's True Reason as an Aura and virtue that's pretty silly. Basically it's taking enlightenment concepts and trying to push them back in time. House Guernicus is known as Quaesator, due to their most common role. Virtues and flaws have a different balance. There's a link between Tremere in ArM and Tremere in WoD. Confidence operates as reroll instead of bonus.
I'm sure there are other, subtle, differences, but the largest are in the feel of the setting. The difference in publishers makes a significant change to the tone of the game.
--- Massive Edit ---
4th to 5th
The differences from 4th to 5th are, as the core book says on 223, "Nothing has changed ... Everything has changed" And it's completely correct. The setting changes from 3rd to 4th are mostly gone, though with a few humorous notes: "The Tremere had a problem with vampires. They fixed it. It's not interesting now." Which is riffing on the white wolf stuff.
Functionally speaking, there are no setting changes that I can tell, and I'm quite familiar with 4th and 5th. While it's possible to use setting books from any edition due to the... rough familiarity of editions, setting books from 3rd and below require "interpretation" that books and adventures from 4th don't. Adventures from 4th are almost wholly compatible, due to the whole "monsters have built-in powers" things. When adapting adventures, power down the opposition, but they can be run from the books as-is.
The largest change in setting comes from the supplements (Art and Academe is a must buy for anyone interested in that time period. City and Guild is a horrible supplement.) There is a much lower focus on "magic" in the world and more focus on the world qua itself. This complements the absence of vis-boosting which means magi cannot trivially take out mundane armies, especially with Realms of Power: The Divine in play. The world as presented is open to significant amounts of interpretation, just like in earlier editions, which suggests the ability to dial for whatever game you want to play. (My current game is mostly focused on resource management and survival in a hostile political atmosphere, and I'm happy to share how I figured out highly-granular accounting schemes for the covenant in a different post if poeple are interested.)
One of the more striking "everything changed" aspects is in virtues. The point system (thankfully) was abolished and virtues consolidated into major and minor. With the exception of Beserk (minor virtue, should be major flaw in how it works out in game play) there are no "trapped" virtues or flaws like previous editions sported. Spell Guidelines have been rationalized and consolidated very well, tough the ranges, durations, and targets have changed slightly (for the better.) There are fewer ones, but spells are roughly at the same power level. Vis is far far less useful in spellcasting and rituals generate long-term fatigue, so they are profoundly not spammable. The changes guide is an excellent reference due to the lack of setting changes.
One of the larger mechanical changes that will impact how players think about the game is confidence. In 4th ed, if you had enough confidence, you could spend it all on every roll and, barring a botch, always succeed and get it back. In 5th, confidence is split into Confidence Score and confidence points (and roughly each realm has an [Hierarchy (Infernal),True Faith(Divine),Fable(Faerie)) score to reflect increasing affiliation with that realm. The magic realm doesn't have a unique one, which reflects the centrality of the core book. Players earn confidence points by role playing and can spend them (as the rules are written) on any stress die roll that happens for a specific event. I run with the house rule that confidence can be spent on anything, which significantly ramps up the rate of power increase.
Combat is lethal, but sane. The rules reward armor and big weapons.
All lab work uses the same mechanic, making it far easier to conceptualize what one is doing in the lab.
To summarize: 5th is more refined and an excellent revision to 4th. It streamlines and "balances" (not in terms of nerfing, per se, but a rationalization of equivalent power). It's quite feasable to port over a 4th edition game to 5th without any real prep. It would not require any significant editing of the world like a 3rd to 4th would have.
In addition to other changes already mentioned:
A big mechanics difference between 4th and 5th ed was a widespread 4th ed house rule was made official, which is that the roll to penetrate magic resistance went from casting total + penetration > MR, to to casting total + penetration > MR + spell level. This made confrontations between magi and magical creatures/other magi/divine/etc very different (and more interesting, IMO), because you no longer just blazed away with your best spells, but quite likely had to use weaker spells to try to penetrate MR (or use sneakier/less direct spells that didn't require MR). So opponents with MR (which could include magi and companions, divine power of kings or clergy, magical or faerie beings, some hedge magi, etc) became more of a threat to magi.
A big difference to the setting actually took place late in 4th edition - The Mysteries sourcebook added a huge number of secret societies each with powerful variant magical virtues. This meant many magi had very variant magical powers, gave an in-game mechanism for virtue acquisition, and many many plot hooks. It made hermetic magic potentially much more diverse, and Hermetic culture and society quite a bit more complex.
These rules were variant in 4th Ed. and became fully integrated into the game in 5th ed (several Houses - Criamon, Merinita, Verditius, Bjornaer) became canonically regarded as examples of mystery cults).
In addition, both 4th and 5th introduced many non-Hermetic magic traditions in full detail, many of which are close to being as powerful in hermetic magic (and some of which may qualify as magi). 5th ed has expanded this concept to include playing magical or faerie creatures.
3rd to 4th has few changes -- mostly in parameters for spells, learning and combat. I always viewed the differences as mostly cosmetic. The big changes are from 4th to 5th.
The Big Change that really altered how we played was that 4th Ed is when one could distill Vis out of nothing with season lab actions. It made the seasona Vis hunts far less important.
There were a number of setting changes in 4, based upon having lost the connection to WWG's old WoD settng.