Is there an actual difference, or are they synonymous?
Let's try some examples for mixtures and solutions. Think about the answers yourself before you uncover them ;-)
We cut carrots, celery, and green beans into pieces and throw them into boiling water to prepare a vegetable soup. Mixture or solution?
It's a mixture, because the pieces of the different vegetables can be retrieved by a physical method, such as picking them with a fork.
Throw a spoonful of sugar into a cup of water and stir until there's no sugar left on the ground of the cup. Mixture or solution?
This is a solution. It it homogenous; even the tiniest part of the water contains the same amount of sugar and there is no way to get back the sugar (unless you boil the water off).
Take a handful of razorblades and a handful of ants. Throw everything in a bowl. Wear gloves! Shake. Mixture or solution?
This is a mixture. You can separate the components with a magnet - or by luring the ants out of the bowl with a trace of sugar water.
Melt iron. Add cobalt. Don't mix with bare hands ;-) Let it cool down until it is a solid again. Mixture or solution?
This is a solution. Solutions do not need to be liquid. They can be solids as well. You can cut the metal block into pieces and mill every piece down to a fine powder and the amount of iron and cobalt in every grain of powder will be the same. Again, you cannot fiddle the components apart by any physical method.