Basically there are two categories of medicines.
OTC medicines (over the counter medicines) are sold without prescription.
The other category is the so called "prescription drugs". You must have a prescription from a doctor to be able to buy those medicines.
Every country has its own regulations as to which medicines are considered "prescription drugs".
For example, Singapore is very strict about that. Only a few basic medicines may be obtained over the counter without prescription in Singapore: medicines like Paracetamol, etc.
On the other hand, Thailand and other countries in Asia don't have such strict rules. For example, in Thailand you can buy many medicines over the counter without prescription, including armour thyroid (natural desiccated thyroid or NDT), aspirin, nurofen, decolgen, amoxicillin, nasolin, tofago, etc.
We live in Thailand, so we can buy over here many medicines over the counter without prescription.