>>1810679They should be tight enough that the chamois doesn't move around on your skin. Whether they feel like a diaper or not depends on how thick the pad is. Note that if you're still getting discomfort, you may still need a different saddle or have a fit issue - the padding just helps prevent chafing, it doesn't magically make a saddle that's a poor shape work for your sitbones.
>>1810718Basically any underwear that isn't cotton (traps moisture against your skin and becomes rough) is fine for cycling. Padded shorts are ideal because they give extra protection for your skin against chafing but aren't necessary unless you're doing really long rides. And for streams that are too deep/wide to ride through I take my shoes and socks off and wade across with the bike on my shoulder.