As far as I know the servo lead size is standardized. But I think only for everything from about the past 5 years and newer. I have a servo from over 10 years ago that is bigger. But it's still three wires so an adapter could be fashioned, assuming it's the same volts.
Unless you get something real exotic, any servo should fit into any RC receiver. As long as it's "hobby" stuff. If you go out and buy a toy from a toy store it'll probably be some weird connection, but the cheap toys don't even have servos.
I guess short answer is "yes" and I don't know why I'm trying to explain it further.
Actually the older stuff was all pretty much the same. There are some newer micro servos that use a different type of connector. You'd have to use a receiver like this one or get adapters for those but for the most part, RCSF had it right.
some branded servos will have a slight tongue sticking out on the side of their connector, its designed to fit within their own branded recievers which have a groove for this tongue. its designed to stop you from putting it in backwards. Luckily if you get one of these the tongue is easy to trim off with your hobby knife so it'll fit into a normal receiver.
The Micro servos (xusme picture) are no standard - at least 4 different - but similar looking connectors are on the market.
The servos are normally Electric compatible - but you might need to replace the connector to fit the receiver.
Futaba style connector has a tab - shoving the signal side. It is simple to cut the tab with a knife or file to fit the JR/Hitec style receivers (connectors with 2 "rounded" corners).
Historically there was Sanwa with different connector - but possible to replace the connector and use the servo.
There has been servos with 4 leads (Kyosho and Multiplex) - not compatible.
You can nomally use at least 40 year old servos with todays Equipment. BUT - check that they move (exerzise them well Before flying).
Check the output of the BEC, voltage needs to be compatable, usually just isnt an issue.
Also if using hi torque servos, you'll need a 3A or above BEC. I allways use a esc with a 3A BEC when the plane has 4 or more 9g servos, just to be safe.
Some servos are VERY sensitive to when to BEC voltage drops a bit low(from drawing too much current from the BEC), and could start to go crazy