Since there are two Senate races at once, and Senators don't have districts...

[Silent3]

...but are voted on by the entire state, how was it decided which Democrat was running against which Republican?

I'm sure this question has been asked ages ago, but I must have missed the answer.

[PatSeg]

1. Interesting question

[LeftInTX]

2. The candidate files for the race..we have two probate judges in our county.

They basically have the same job

[zaj]

3. There is a filing process. I'm sure they filed for...

... the seat they are now running to fill.

[Johnny2X2X]

4. There are seats, you run for the seat

They are named seats. GA-4 and G-5 I think.

[Claustrum]

5. There were 2 different primaries. One was a democrats only primary for race with Perdue.

Then there is a second jungle primary that had 10+ people running in Nov (the general election). The candidates filed for the corresponding primary.

[LisaL]

6. One race is a regular election, the other race is a special election.

NT

[brush]

11. Thank you. This is the answer. Perdue's six-year term was up...

the Loeffler race is, as you said, a special election as she was appointed by the governor because of a resignation.

[BGBD]

7. Just whichever you file for.

Those things were likely coordinated through the DNC to ensure a quality candidate in each race.

[Alex4Martinez]

8. Every State has two US Senators who represent the whole state, run different 6-year election cycles.

Loeffler was appointed to fill a seat last year that will expire at the end of 2022.
Perdue's seat expires this year.

Typically, each state's two US senators are in 6 year terms that are staggered by 2 or 4 years.

https://en.wikipedia.org/wiki/List_of_current_United_States_senators

[Silent3]

9. I knew that they were normally staggered like that...

...which makes it clear who's running for what, since there's normally only one Senate seat per state up for grabs.

[Alex4Martinez]

10. This is a peculiar year because Kemp appointed Loeffler.

So I guess the stagger will return with Warnock having to re-run in 2022 as the incumbent, and Ossoff beginning a fresh 6-year term.
Perdue's term was expiring this year.