Legend is that Satoshi worked on the puzzle alone.
Then later, Satoshi contacted others for input that contributed to the whitepaper (Wai and others).*
After the whitepaper was released, one other individual came along to help Satoshi build the software (Sirius).**
After the foundation was established around mid 2010, many others appeared to help contribute (Gavin and others).
Bitcoin Core is the most recent version of the software, starting around 2013.
Satoshi never contributed to Core (that we are aware of).
1st Client: Bitcoin-Satoshi
2nd Client: Bitcoin QT
3rd Client: Bitcoin Core
Satoshi may not have contributed to QT either.
The following should help answer some questions:
https://bitcoin.org/en/version-history^ this is the most factually accurate.
just to add a few clarifications
*satoshi did inform his 'references' that he was developing something that used parts of their concepts, though they did not really get back to him.
**by February 2009 there were a handfull of devs helping out. (hal finney was there within the first week of bitcoins public release in January)
by the end of 2009 there were over a dozen+