Hy,
Now that you have indicated the resistor size I can assure you that smaller resistors are 125mW and the bigger resistors are 250mW; neither are half watt.
The reason why the issue even arose is because of the vendor’s loose and unqualified description. The only way to establish what a part can do is to get the exact part number and check the datasheet. The trouble is that many second line retailers sell unbranded and unspecified components. Their description are also loose to say the least. The rule is never buy anything until you have established it’s specification- vendors descriptions are riddled with errors anyway (not so the mainline vendors like RS, Farnell, Mouser etc, but, even they make the odd mistake). To make matters worse there are even errors on data sheets, but rarely.
The other thing is that the rating of any component depends on the conditions. For example, the rating of a resistor may be 1W, but that may be at a body temperature of 25 deg C. In practical terms, unless the resistor were immersed in a bath of oil at around 10 deg C, this is a meaningless specification. What you need is the resistor dissipation in free air at 25 deg C.
But, if the resistor is mounted in your equipment and the air in the equipment is 50 deg C, a fairly normal temperature, then a 250mW resistor may become a 125mW resistor. The controlling factor, with all electronic components, is the maximum temperature of the active part: in the case of a resistor, the ceramic insulating tube (body) and the spiral film (resistor) deposited on it. With a transistor the active part is the semiconductor junction, which typically must not exceed 170 deg C or the transistor will be destroyed or permanently damaged.
As has already been said, there are a number of different resistor types: some information here:
https://www.electro-tech-online.com/threads/transistor-equivalent.146091/page-27 Post 530.
I’m not sure how much you know about electronics; just in case, here is a bit of useful basic theory about resistor power dissipation:
(1) The power dissipated is a resistor is: the current flowing through the resistor squared, multiplied by the resistor value. So for example, if you had a 10 Ohm resistor with 2 Amps flowing through it, the power dissipation in the resistor would be (2 * 2) * 10= 40W
(2) The power dissipated is a resistor is also: voltage across the resistor squared divided by the resistor value. So for the same example, if you had a 10 Ohm resistor with 20V across it, the power dissipation in the resistor would be (20 * 20) / 10= 40W
(3) The power dissipated in a resistor is also: current flowing through a resistor times the voltage across the resistor. So again for the same example, the current flowing through the resistor would be 2A and thus the voltage across the resistor would be 20 Volts. Thus 2 * 20 = 40 Watts again.
There is a simple way to check if a resistor is OK as far as power dissipation goes: put your finger on it- if you can’t quite keep it there that is around 70 deg C and is a good design maximum surface temperature; anything higher is unwise. This is not the case for certain power resistors which can run at around 100 deg C.
After all that, I bet you wished you had never asked. I will get my coat now.
PS: you can check for yourself what wattage ratings your resistors are by using the formlae above and the finger test!