A resolution is the act of finding a solution to a conflict or problem.
A goal is something that you are trying to do or achieve.
When you look at the definition of a resolution it comes across as a negative thing. You need to set a resolution in order to solve a problem. My weight is a problem so I need to resolve to lose it.
Whereas a goal is something more positive. Something that you can be proud of. Something that you achieve. My goal is to exercise in order to lose weight.
I use weight as an example because people make such a big deal about starting weight loss routines at the beginning of the year, it's the most identifiable, and most often heard, new years resolution.

Pay off all of my debt, excluding my car and student loans.
Maintain a savings account.
Fix my credit so we can buy a house.
Meet Josh's kids.
Travel somewhere in the US that I've never been before.
Go out of town, on a (quasi)vacation, at least once a quarter.
Exercise for a half an hour, three times a week.
Blog once a week.
Become a senior property manager.
Get my Oregon brokers license.
Take PJ on a date once a month.
Go on a date with Veronica once a month.
Eat someplace we've never eaten before with Josh once a month.