I like Starfinder, so I decided to write up this introduction to the system because some other people might like it too once they see what it's like.
A big thing to remember is that Stafinder is NOT Pathfinder in space, it is a different take on the D20 system. The base lore is basically Pathfinder in the future, but there's a lot more to it than that and this post will just be about mechanics.
Instead of just making a big list of the differences, I'll break it down into sections (mostly like in the book but now you don't have to read it to know what's going on).
Ability Scores: This is about what you'd expect except that point-buy is the default (with 10 being the base number for each stat) and rolling is an optional method. Every class has a key ability score so you know what the most important stat is for you right out of the gate.
You gain ability score adjustments from your race (PF standard here with a total modifier of +2 per race). In addition, you get one point from your theme.
Themes: Hey look, we're already at something new. Theme is just what it sounds like, it's a central theme for your character (you can choose to be "themeless" but that is pointed out to be a less powerful way to go so don't do that).
The theme choice is a combination of background/training/goals/destiny/however you want to flavor it. There are 9 themes (not counting themeless) in the core book and more books add more themes. Each theme grants you benefits at 1st, 6th, 12th, and 18 levels as well as a +1 bonus to a specified ability score. If you want to be an Outlaw you pick the Outlaw theme and get some Outlaw specific freebies and don't have to spend skill points or feats or whatever trying to make yourself more of an "outlaw".
Races: As I mentioned, races use the PF standard of having a total modifier of +2 (so humans get +2 to anything and everyone else gets two +2 bonuses and a -2 penalty). The only new thing here is that races also have a HP section. Humans start with more HP than rat people aliens and lizard people aliens get more than humans (2-6 is the standard range).
Hit Points: Hit Points are statically granted, not randomly generated. You get HP from your race and then the listed HP from your class each level. In addition, at every level you gain Stamina Points on top of HP and Con grants extra Stamina, not HP. Stamina get reduced before HP. In addition, nonlethal damage is just like regular damage except it can't reduce you below 0 hp so it isn't tracked as a completely different type of damage.
Resolve Points: Another new thing, and definitely not Action Points. Resolve points are either used to activate class features or to help you not die, and how many you have is based on the ability modifier of the key ability score of your class.
Classes: There are 7 classes in the core rulebook with a few more added in supplements. Each class has a key ability score (some let you choose your score between two options). This basically means that every class has abilities which are based on that score (so you don't have a fighter equivalent which cares about stats for combat but doesn't have class features). There are no dead levels (at a minimum you gain a whole new level of spells that level).
Classes are very open-ended in way that I really like. Each class has some core abilities (spells or a robot companion or bonuses with skills) and then you get a couple of lists to pick class features off of which drastically reduces cookie cutter builds (and this is good because multiclassing is allowed but there are no prestige classes at all, it's not a thing).
In addition, everyone gets Weapon Specialization for free at 3rd level for a group of weapons so they can kill things in combat (and SF weapon specialization is bonus damage based on your level). Also, ACFs exist but they're called Archetypes and they aren't class specific. The Archetypes replace specified class features based on your original class and then you gain the new class features. If you want to focus on being cybernetically augmented or a sage or a divine champion then there is an Archetype for that and you don't have to try to shoehorn it into whatever build you're already going for.
Lastly, spells cap out at level 6. Starfinder does not have a Wish equivalent, high level spells are just not in the game at all (as are most of the game breaking spells in general).
Skills: This is basically PF standard. Maximum of 1 rank per level (doesn't matter if it is trained or untrained) and you get a +3 bonus for trained skills with ranks in them. There are only 20 skills, and Profession is the only one where you pick a specialization. All knowledge skills are now their own actual skill.
Equipment: Two things first: WBL is still a thing and Starships don't count as gear and aren't a part of WBL. The big thing is that every item has a level. If you're level 6, you should have weapons of around level 6 (which do more damage then level 1 weapons). It is the same with armor and everything else. Armor worn by level 20 characters is better quality than armor worn by level 1 characters, it isn't just the same armor with +10 worth of magic crap on it.
Magic and magic items still exist. Magic weapon enhancements are called fusions (and there are rules for swapping them around) and armor can have upgrades which are not magical. Weapon fusion cap is based on the item level of both the fusions and the weapon, armor upgrades are limited by the upgrade slots in the armor. There are also augmentations (aka cybernetics/biotechnology), both technological as well as magical (Necrografts!).
Combat: There are now only 2 armor classes, Kinetic Armor Class and Energy Armor Class. Different attacks target different armor classes and each armor has a value for both (though that value might be 0, and the higher the armor level the better the values). No more of this flat-footed/touch stuff. Saving throws are as normal.
Actions are pretty much as expected except Full Action has replaced Full-Round Action and a Full Action takes up your Swift too. Immediate actions are gone and there is now the Reaction action (Attacks of Opportunity are a Reaction).
Vehicles also get their own rules which include rules for chases.
Starships: Having a starship is pretty much just assumed, as I mentioned it doesn't even count against you in terms of gear. Of course, some premade (or homemade) adventures will make you earn one in some way or another. FTL travel is done in the Drift which reminds me of nothing so much as the 40k warp except it isn't full of daemons and won't drive you insane.
Starships are complicated, they get a whole character sheet to themselves. They have tiers, and their tiers are more like CR than Item Levels (including factional tiers). However, the difference between starship tiers is bigger than CR. You can either just pick a starship, or build one yourself. Building one doesn't involve money in any way, each tier gains a specific number of Build Points. Each frame (basic type of ship such as racer, shuttle, transport, etc.) costs a specific number of Build Points. Whatever points are left over are used for components (power core, thrusters, drift engines, weapons, etc).
Starship Combat: Honestly this is the most complicated part of Starfinder. As long as you are a part of the crew, you get to pick a role (captain, pilot, gunner, etc). Each role gets to take an action during combat so everyone gets to do something.
Starship combat is done using a hex grid. Starships have four firing arcs (forward, aft, port, and starboard). Different weapons are in different arcs. There are stunts you can make (with handy visualizations) and checks are required. Up and down are not included, but this definitely is something that would be difficult to run without a battle map.
Thoughts? Was this useful for anyone? Is there anything that I should delve more deeply into?