I use the two terms interchangeably, therefore I don't process a difference between "gods" and "spirits." Well, that's not precisely the case. Let's get into the nuances of that, because it relates to how Paganisms approach deity in ways that are different than, say, the monotheisms folks in the West are more familiar with.
In the monotheistic traditions, what "god" can mean covers a narrow territory. When you have polytheism, the range of things that "god" can mean covers a considerably broader territory. At the end of the day, if we want to be culturally inclusive about defining what "god" means, a god is basically something a culture deems worthy of worship. It's like a title applied to something, similar to "doctor" or "professor." Such titles designate a role and a relationship. In the case of gods, the role is "worthy" and the relationship is "worship."
What does it mean to be "worthy?" It varies from tradition to tradition, but broadly speaking, it means something is held in high regard, deeply valued, or respected. What does it mean to have a relationship of "worship?" Again, it varies from tradition to tradition, but broadly speaking it means you demonstrate respect by doing things such as expressing gratitude, appreciation, or celebrating.
As far as I'm concerned, if something in your life is deemed worthy of worship, those are your gods. Honestly, the word used doesn't much matter. Gods. Spirits. Ancestors. Kami. Theoi. Whatever. The specific terms vary from culture to culture too, and it's the substance that is important. But this does mean I don't really see much of a distinction between "gods" and "spirits." The word "spirit" or "ancestor" could be a word used to designate something something worthy of worship just as easily as "god" can be.
There's a bit more to it than that, but this is the important bit, I think.