Safety pilot isn't a category of flight time, but one can log PIC or SIC as a safety pilot, depending on who is acting as pilot in command, and both pilots can log the time in a light single that's otherwise certificated as a single pilot airplane.
Who is manipulating the controls, who is the acting pilot in command, and who is qualified for what, determines who can log what time, in a light single (or any aircraft). Consequently, there are times when both pilots may log PIC, the pilot not flying may log PIC, the pilot flying may log PIC, and even times when no one can log the flight time.
I have known active duty pilots that did a little flying on the side, dropping jumpers in a Cessna 206, to gain a little extra flight time.
If you're going to pay for the time, the least expensive way to knock it out is to go play safety pilot, and split the cost. One pilot flies "under the hood" with a view-limiting-device, and the other pilot acts as pilot in command, and also as the required safety pilot. The pilot flying, under the hood, logs PIC as sole manipulator of the controls, and the pilot acting as PIC and safety pilot, logs PIC as the pilot-in-command of an aircraft requiring more than one crew member under the regulations under which it is operating: 14 CFR 91.109(c).
https://www.ecfr.gov/current/title-14/chapter-I/subchapter-F/part-91/subpart-B/subject-group-ECFRe4c59b5f5506932/section-91.109
One should be aware that some operators consider safety pilot time to be stretching the regulation, or view it as an end-run around actually serving as pilot-in-command. It's perfectly legal but how it's viewed varies among operators. Some may see it as padding one's logbook.