Yes, Patience and Equanimity have subtle differences. Patience can be just quietly enduring something, it may not necessarily have wisdom with it. For example, we are just patient and we "endure" something until it's finished whereas Equanimity doesn't suffer in the process of being patient. To have true Equanimity, there has to have a certain amount of wisdom to understand that some things are beyond our power to control, whereas a person may be patient but not necessarily equanimous to the situation.
Equanimity is more difficult because it depends on a certain amount of Insight. There are a lot of people who have learned to be patient but not necessarily equanimous, they still don't like the fact that they have to wait but they patiently wait, whereas equanimity has less preferences involved in that situation, it's not just enduring something.
For instance, we could bring up the situation of a person with pain, a person with a strong will power and determination can endure pain but that's different to observing the nature of pain moment to moment and developing Equanimity and Insight into it. So in that simple example perhaps you can see the difference.