Are disc brake rotors interchangeable between brands? I have Tektro HD-R310 brakes, with center lock rims, using the new and only center lock rotors from Tektro TR160-35

Well after 2 months of driving in winter, i already notice some rust on the rotors (and i do clean my bike often)

That never happend on my other bike which i rarely clean with shimano slx + rotors.

So my question would be, can i use better quality shimano rotors with my tektro brake? Only problem i can think of would be the pads type (resin), which needs to be compatible. I'm still on the original pads but will switch to "SwissStop Disc34 RS" after they are worn out.
tldr: be sure new rotor works with metal pads or get a set of resin pads.

Generally, disk brake rotors of same diameter are thought of as cross-compatible, but there are some edge cases when this might not be true:


Rotor thickness might not be the same across manufacturers and disk brake calipers might be designed with thicker/thinner rotor in mind. Examples: Tektro TR180-16 / TR203-16 has thickness of 1.85mm and TR180-17 / TR203-17 is 2.3mm thick; also, see Lennard Zinn's piece on the subject.
As you already noted, rotor manufacturer might require or recommend to use certain kind of pads. Examples: Shimano SM-RT56 is compatible with resin pads only (literally written on the rotor) while SM-RT64 can work with both resin and metal pads. More exotic rotors might also require a matching set of pads.


Let's put all of the above to your case:


A relevant quote from Zinn's piece:


  Shimano rotors are made 1.8mm thick and should be replaced when the
  thickness has been reduced to 1.5mm.  Since 2010, the 1.5mm minimum recommended rotor thickness has been printed on Shimano rotors.


Based on published TRP rotor thickness, I assume TR160-35 is most likely 1.85mm thick. According to Shimano, a 0.05mm thickness difference is in a range of expected rotor wear, as per quote above. So, no problems here.
Tektro HD-R310 comes with "Metal Ceramic Compound" pads. That means the new rotor should either support metal pads (like top of the line SM-RT900) or you should get a set of resin pads if new rotor requires these.