As long as the new tube matches the rim size, width, and valve, you're fine.
"thin" tubes are simply made of thinner rubber and therefore weigh less. The difference is maybe 50 grams between a regular and a light tube, and another 50-100 from a regular to a heavy tube.
A thinner tube is slightly more likely to puncture, where a heavier one can often shrug off the same damage and retain air.
A thinner tube could "leak down" slightly faster than a thicker tube, but it might need re-inflating every 5 days rather than every 7-10 days. The difference is minimal.
In short, as long as the new tube has
- the same valve style
- the same diameter
- and covers the width of your tyre, then you're okay.
If the old tubes still hold air, stick one in your on-bike spares bag along with levers and a pump.