What's the difference?
With thanks to Dorota Rocinska for the suggestion.
Two similar words with similar, but not quite the same meaning.
Resilience is an uncountable noun, the adjective form being resilient.
If you show resilience to something - even a lot of resilience - then you are strong and are not easily affected. As a person, you could be resilient - or show a lot of resilience - to colds and flu, or even illnesses in general. It means that you are very rarely affected by them, and so you should remain fit and strong. This doesn't mean that you are not affected; just not as badly affected as others.
Now if we talk about things that are resilient (or show resilience, of course) this means that it is strong and not easily damaged. Spring steel, for example, is a resilient material: it is strong and not easily damaged by being hit, stretched, or squeezed.
The word also suggests that if you do suffer from some kind of unpleasant or damaging effect, then you are able to recover quickly and easily. For example, Polish banks proved more resilient to others around the world when there was a global financial crisis at the end of the 20th century.
But when we enter the world of material science (which was what I believe was being suggested by Dorota), then resilience is the ability of a material to absorb energy when it is deformed elastically, but is then able to release that energy upon unloading; for example, a spring, or springs in a bed. These new mattresses have a lot of resilience and so can last for years. As a result, particularly after being in regular or continuous use, it will remain strong for some time, but it will become damaged eventually.
Now resistance has many meanings. As an uncountable noun, it can mean refusing to accept a new idea: There has been resistance from the local community about the route of the new road. It means to fight back against someone attacking: There was no resistance from the demonstrators towards the army. It can mean the ability of your body to remain unharmed or unaffected by germs or diseases: I'm on a course of immunisation which will help build some resistance against dust and pollen. we can add wind or air as adjectives to the word to describe a force that slows down something: Wind resistance. In physics, this is the ability of a substance or an electrical circuit that can stop the flow of an electrical current going through it. Rubber has electrical resistance. Then as a singular noun, a resistance is an organised group of people who are involved in activities against the people in power. The French resistance during the Second World War.
But like the above, I suspect Dorota is after the material science meaning. Put simply, resistance is when something has the ability to not get damaged by something and is able to keep its shape and appearance very much the way it was before the force that tries to damage it; if you like, a force that tends to oppose motion. This rusty bolt is showing a lot of resistance - I can't unscrew it!
So in summary (if we're going for the scientific meaning):
resilience: to be strong and not be easily affected (but can still be affected, such as minor damage, but not enough to affect its performance) by a thing or force over a period of time, usually when talking about a continuous force.
resistance: to not get damaged, to be able to keep its shape after being hit, impacted by something, or being given force to move.
Here's a comparison:
You know, that car's been through a lot in the last ten years - 300,000 kilometres, two accidents, change of axle, but it's still running very well. It's showing a lot of resilience.
Despite the collision, there doesn't seem to be much damage. That car seems to show some resistance to that kind of thing.
I think it's also worth looking at other synonyms, but if you want to look deeper into the meanings then a scientific dictionary will be needed:
Hardness: the property of a material that enables it to resist plastic deformation, penetration, indentation, and scratching.
Toughness: a measure of the amount of energy a material can absorb before it actually fractures or breaks.
Stiffness: to describe a material that is not easy to bend or be deflected.