A pushchair carrycot is designed for your baby to lie completely flat, which is what paediatric guidance recommends for newborn sleep, including on the move. A car seat, by contrast, holds baby in a semi-upright, curled position — fine for the actual car journey, but not recommended for long naps once you’re out of the car.
The rule of thumb many health visitors give is: if the journey involves driving, use the car seat for the drive, then move baby to the carrycot (or a flat surface) as soon as you’re walking rather than driving. Avoid long stretches of a young baby sleeping upright in a bucket-style car seat outside the car.
If your travel system only came with a car seat adaptor and no carrycot, it’s worth checking whether a compatible carrycot is sold separately — many brands sell it as an add-on rather than bundling it by default.