Let's assume that they are both made with chicken, and that the curry is a traditional Indian curry, with tomato and traditional spices, not with "curry powder" tossed in it.
Various articles claim to describe the differences, but they disagree with each other.
Recipes for both use the same seasonings, and appear pretty much interchangeable, except that curry often has coconut-something in it, and tikka masala is heavy on butter and cream.
How are they actually supposed to be different?
The difference between curry and tikka is more down to the preparation and way the dish is cooked, rather than the core ingredients, although they may share many common factors.
For instance, the meat for a curry might be marinaded in a sauce (masala) beforehand, or it might just be pan fried along with onions and garlic with the cooking sauce built from tomatoes, yoghurt, stock etc. and the meat (Chicken, beef or lamb) finally cooked off in this sauce. So traditionally, a curry is cooked in a pan or casserole pot.
On the other hand, a tikka will almost always be marinaded beforehand, generally in a mixture of oil, yoghurt, garlic, lemon juice, ginger and spices for at least an hour, preferably overnight. The meat (Generally chicken, although lamb is also used) is then placed on a skewer and cooked vertically in a traditional tandoori oven, although a Western adaptation would be to grill or oven cook the pieces. Frequently, food colouring is added to the chicken to give a vibrant red, yellow or orange look, something that is not done in a traditional curry.
Once the tikka meat is cooked it may be served with a side salad, or added to a tomato and cream based sauce which then forms a very modern dish, chicken tikka masala.
Effectively, the difference between a curry and a tikka is stewing/braising versus roasting.
'Curry' is a very general term, generally applied on cuisines from an outside perspective. In a particular area there may be a 'default' curry but this will differ widely in different places and contexts – "traditional Indian curry" is an understandable misconception, like saying there's a specific dish which is "standard Italian pasta".
Tikka Masala is a more specific dish although there will be variation, a staple of British 'Indian' (which also includes Bangladeshi and Pakistani) cuisine.
So as noted in the comments, tikka masala is a type of curry.
