Causes of diarrhea fall into two groups. In the first group, the problem lies in the small intestine, and in the second, in the large intestine or rectum. Since your pet is presenting with loose stools and is also vomiting, the problem with your pet lies in their small intestine.
Diarrhea in cats can be caused by eating the wrong thing (rotten food from the bin) and the problem can be fixed by withholding food for 24 hours and giving the animal Imodium (0.2 mg/ml) at the rate of 1 ml for every four pounds of weight three times a day.
When you take your pet to the vet, take along with you a stool sample so they can quickly run tests. Make sure your pet is drinking enough water so as to not get dehydrated.