Matching Breaker to wire size

Yesterday I inspected a house that had a double 60 amp breaker serving a sub panel with 8/3 wire. I flagged it as the breaker was too big or the wire too small. When I checked the code later, I found the code calling for #8 wires with 60 Amp breakers for an electric furnace but also called for 40 amp breakers for the electric stove.
Is this a quirk in the code?
What I really want to know is the min size wire for each size of breaker. I though I had it figured out but this has me puzzled.:???:
PS this is the Alberta code I’m reading.

Many appliances have their own ratings, but in general, a 60 amp load side panel should be fed by #6 or larger CU.

The biggest exception to the general rule is motor loads like the A/C compressor. They have internal overload protection so the branch circuit O/C device is only providing short circuit protection and that can be at a higher level. A short will present massive amounts of current that will trip the breaker long before any damage is done. Overloads are more sinister since they slowly cook the conductors. That is where the 80% rule and 240.4(D) come from.

Look at the nameplate on an AC unit when you get a chance. You should find (at least in the US) a listing for Maximum Circuit Breaker size and another For minimum ampacity. You are allowed by NEC to breaker for the maximum and wire for the minumum. Therefore, it is possible to have #8 wire on a 60a breaker. Since ranges, dryers and water heaters are mostly resistive loads (heating elements) this does not apply.

As Greg said, motors and A/C units follow a different set of codes. The installation in question is a feeder.

DO NOT go looking for a standard wire-to-breaker chart. One does not exist. If you find one, it is wrong. Or at least not always correct.

#8 in NM cable must use the 60[FONT=Arial]°c column. This give it a 40 amp rating
#8 THHN conductors in conduit can use the 75[/FONT][FONT=Arial]°c column. This gives it a 50 amp rating.

Also, ranges, ovens and cooktops follow different rules. ANY unit rated at 12kw or less can be on a 40 amp circuit, so you may find one that seems too large for it’s circuit. It is likely not.

THHN conductors have a 90[/FONT][FONT=Arial]°c rating, but we can pretty much never use this column for actual ampacity since there are very few terminations rated for 90[/FONT][FONT=Arial]°c and we must use the weakest link to figure ampacity. This is why we use 75[/FONT][FONT=Arial]°c for conductors since most terminations are rated at 75[/FONT][FONT=Arial]°c.
The 90[/FONT][FONT=Arial]°c column is used for adjustment factoring, such as derating.

Thanks for the information.
The more I learn the less I know.
I did not provide all the info on the house wiring.
It had a double 60 Amp breaker to a sub panel with 8/3 wire. The sub panel had 5 - 15 amp breakers.