Sauce – use cream cheese in a sauce

Quite simply, it's the fat content.

Whole milk or "full-fat" milk is 3.25% fat by weight. Heavy cream is 36-40% fat by weight. These two products are at opposite ends of the fat spectrum, and there's very little difference between 1% and 3% when it comes to an item such as caramel sauce, for which the optimal ratio is about 50% fat. (A little butter can boost the fat content from 40% to 50%).

You might be able to substitute standard/single cream (18-20%) or maybe even coffee cream/half-and-half (10%), but any lower than that and you're just making sugary milk.

Other alternatives to (possibly) get it thicker:

• Use (much) less milk; I'd advise not attempting a direct substitution, just find a recipe based on milk. Even the best milk-based caramel sauce will still be substantially runnier and/or grittier than a cream-based sauce.

• Considering that butter is 80% fat and homo milk is 3.25%, you could use a mixture of (approximately) half milk and half butter that would emulate the fat content of heavy cream. I've never tried this personally, and I suspect that the flavour might be a little off, but at least it would be closer to the expected texture.

• Try a reduction (simmer off the water in the milk). You'll be simmering a long time, and you'll have to watch it very carefully to make sure it doesn't burn, and you'll probably have a nasty stuck-on mess to clean up in the pan afterward, but it will thicken.

This is 100% about flavor. Butter will give you this, EVOO will give you that, ...

Butter will give you a 'richer' taste, whatever that may mean for you. Extra Virgin Olive Oil, generally speaking is far more powerful and may become overwhelming. Any other oil will give you a different taste profile.

Sunflower oil may be the most neutral and therefor the most appropriate for Alfredo sauce. Cannola oil may be another neutral oil, but I've never used it myself.

Generally speaking, an oil is an oil is a fat (for emulsifying).