The other two builds are stargate into two gates into expand, but that can be more volatile. The second build is doing something similar to the first twilight build but with a robo instead of twilight for faster immortal/collosus.
PvZ - 2018's "standard" was opening stargate with an oracle or two and a phoenix into the 4 gate archon drops but those started dropping off a bit due to the old nydus and the fact that people realized immortal timings were just better than actually trying to go late vs 70+ drone zergs with nerfed carriers.
You'll see a lot of 2 base immortal/sentry soul train type deals or adept plays because of it. If you'd like a build that's similar and can transition go for the 1 gate > expand > twilight and robo > 3 gate > DT shrine build. You get like 3 units out of the first gateway and make a prism right away then warp in 4 DTs (or 4 chargelots then 4 DTs). You can play with the 4 DTs or morph them to archons if you prefer. It's pretty easy to transition into an immortal all in or a 3rd if you prefer, just need to make sure you prioritize immortal production right after the DTs and make sure you are constantly hallucination scouting to watch for the zerg tech choices as a muta switch/swarmhost will straight end the game if you aren't ready. If they go roach or hydra/lurker you just abuse double robo and then get storm.
PvP is a little harder as it's more volatile. Gemini posted this some time back.
Most common setup is 2 gates, which produce a combination of 6 units depending on preference and what your tech choice affords you, and then getting a tech choice (twilight with upgrades, a twilight DT shrine, a stargate, or a robo and then your nexus before really pumping much out of that tech. You can put the expansion before tech but you need to watch out for 1 base play and utilize shield batteries properly and have a good defense. Proxying is VERY common in the meta right now due to heavy realiance on hallucination scouts and the fact that they might not be able to scout your tech early enough if they don't find it.
Strengths and Weakness of the Gateway Units
Adepts - Gas light so you can produce army while teching up. In PvT the adept is the best unit at defending the 1 reaper scout/harass. It can shade across the map to deny the terran natural and is generally good vs all the early terran units. In PvZ it lets you bully lings, check zerg drone counts, zerg 3rd base timing, and if they are going for an early lair or cheese builds. It can also be used as drone harass. In PvP adepts can check around the map for proxies pretty easily and you can threaten to shade into their base and keep them defensive. They also body up sentries very quickly leading to favorable gas trades early on. They are quite worse in fights than stalkers and will die ridiculously fast to stargate units.
Stalker - Strongest/most flexible combat unit early on. In PvT groups of stalkers are generally best at defending early harass and aggression, and you obviously need some to cover starport based play. PvZ stalkers only sometimes come out as a way to deny overlord scouting. Many builds will cut stalkers and go for cheaper adepts or get sentires to build energy for a timing. Post immortal production you can sometimes pick up blink to aid in fighting some of the zerg tech switches. PvP stalkers are important because they win the actual fights out on the map early on and they are the only thing can effectively fend off oracles but they typically suck in the midgame and lose out on raw combat ability to archon/zealot/immortals.
Sentry - Fit into builds unique due to heavy gas cost and low mineral cost. These are made almost entirely for the hallucination scout (and the emergency forcefield.) In PvT you won't typically have more than 3 and usually 1 or 2 is fine just for guardian shield and hallucination If you make a sentry you should be using it for hallucination and not burning force fields you don't need. PvZ you want several so you can constantly hallucination scout to make sure to keep an eye on zerg tech in the midgame, and force fields make immortalt significantly more imba vs roaches and ravagers. In PvP you will most frequently see just 1 sentry early on to get that scouting. If you mine gas a little more aggressively at the start your 2 gate can prooduce stalker/sentry/WG as soon as cyber finishes to get a 3:00 minute hallucination scout to see tech (or a lackthereof). If you have sentries and aren't hallucinated frequently you are using them wrong - for the most part.