That's not how you make it sound. You make it sound as if it's the same thing yet for the person you say it to as if they wouldn't know the difference.
To me praying is speaking or appealing to god. Thinking of a person is just that - thinking about him/her. Whether someone knows the difference is immaterial. If I said I would pray for someone I would pray for them, if I said they were in my thoughts then they were. I did whatever I said I would do. I would respect the beliefs/cultural practices of whoever I was caring for. I was fortunate that I never encountered a situation where there was a conflict that I could not stomach. I would not do something that would cause harm to my patient.