We have the Graco AFFIX Backless Booster Car Seat with Latch System, but our new babysitter's car does not have LATCH. Would there be any difference between using this seat without LATCH (just with the seatbelt) and buying a LATCH-less booster seat?
With car seats for younger children (infants or toddlers), there are straps which hold the child into the car seat and then an additional system to secure the seat to the car. This used to be with a regular seat belt, but in modern vehicles is more commonly with LATCH. (Having once fed a seat belt through a toddler seat in a car without LATCH, it's quite obvious that the LATCH system was a terrific innovation for its ease of use.)
In contrast, the child is being restrained by the car's seatbelt when sitting in a booster seat.
A booster seat is a firm cushion of foam or plastic that raises the child higher in the car to improve the position and angle of the shoulder belt. Source
Booster seats are a type of child restraint that do not have a five-point harness system, but rather rely on the vehicle seat belt system to keep your child restrained. The booster seat elevates your child so that the vehicle seat belt is positioned properly over your child. Booster seats should be used in the rear vehicle seat with a lap and shoulder seat belt system, never a lap belt-only. Source
The LATCH connection for the seat you have isn't providing any additional restraint -- imagine your child sitting it in without a seatbelt, it's just as easy to fall forward in the case of an accident whether the seat is secured to the car or not.
The key thing is to make sure the booster seat is is used with both a lap and shoulder belt.
I would personally purchase an additional (LATCH-less) booster seat for the babysitter's car, so it's always there and you won't ever have the problem of forgetting to transfer the seat. We actually own four booster seats for two kids, to cover a range of possible transportation situations -- the extra set purchased after one frustrating week where we forgot to transfer seats every single day.
Anchors for booster seats are only for convenience, not for safety.
he LATCH system, as mandated in US vehicles from 2002 onward, supports a total combined weight of both child and seat of no more than 65 pounds. I found this information on Consumer Reports.
Depending on the weight of your car seat or booster seat, this may mean the LATCH system only supports children weighing anywhere from 32-50 pounds. In these cases, it's necessarily safer to use the seat belts to secure the seat, rather than the LATCH system.
The reason LATCH was developed was not because it is inherently safer, but because it's inherently easier to secure the seats properly.
Securing seats properly with the seat belt straps is more difficult, so more care must be taken in doing so. However, seat belts do not have the surprisingly low maximum supported weight that LATCH systems do. Seat belts are designed to safely secure adult passengers of various weights.
Booster seats that only use the seat belt to secure the child, and don't secure the seat, gain no additional safety benefit from the LATCH system. It's there mainly for convenience: the child can get in the seat themselves without it shifting and it doesn't become "free" when not in use. Children in this types of seats are more likely to outgrow or already by over the weight limits of LATCH systems.
If the booster seat is not in use, it should be anchored with the LATCH system or stored in a safe area, in order to prevent it from becoming a hazard during a car accident.