A:
They are very similar but not always interchangeable.
A person can do the action of calming/soothing or making calm. To be “calm” can be a quality or a trait of their personality. To be “soothe, soothing” is usually NOT a personality trait of a person.
An object CANNOT do the action of calming or making calm but it can have the effect on a person to calm them. Same with soothing. An object can have a soothing effect or it can soothe tension or emotions.
These are all used frequently and sound natural:
“You are a calm person.”
“You know how to calm a situation.”
“You have a calming effect on me.”
These are unnatural:
“You are a soothing person.” (you can say this but calm is more natural and common)
“You know how to soothe a situation.” (you can say this but not natural or common)
“You have a soothing effect on me.” (you can say this but we use calm. Calm is more common)