The dictionary gives the same translation; "relaxing(ly)", but I want to be sure that you can use them interchangeably.
It seems, erholsam is more for long-term activities (or passivities) and their long-term effects, whereas entspannend is used usually in context of short-term things:
Here are examples for the typical use of the two words.
Der Urlaub war erholsam.
Whereas Der Urlaub war entspannend would be a bit unusual to say.
Der Besuch im Thermalbad war entspannend.
Whereas Der Besuch im Thermalbad war erholsam would mean that the effects are explicitely lasting for a long time. Which is possible but a bit unusual.
Marias Gesellschaft ist immer sehr erholsam für mich.
Here we emphasize the long term effect, evident explicitly also for a long time after Maria left.
Marias Gesellschaft wirkt auf mich immer total entspannend.
Here the focus is on the momentary situation, i.e. during Maria's presence; not so much afterwards.
Yes, there is a difference, but it is a really fine difference that translation programs are going to miss. Let me explain.
"Ich entspanne mich beim Kochen.“ - I relax by cooking. "Ich entspanne mich beim Fahren." _ I relax by driving. "Wie entspannst du dich?" - How do you relax?
These all mean that you are tense and you do something to get relief. You need to remove the tension. You need to calm down and relax and find your inner peace, a person is calming down.
This is also a type of relaxing, but it comes from a different need. A person might be worn down, tired, over-exercised, sick. A person needs something to help them recover and get back to their top-state of existence.
"Schlaf ist erholsam." - Sleep is relaxing. "Urlaub ist erholsam." - Vacation is relaxing.
One leads to the other
The internet is full of articles about using exercise to relax to get a good's night sleep. For example, "Entspannungsübungen für erholsamen Schlaf", The literal translation is "Relaxation exercises for a relaxing sleep". In other words, Entspannung (relaxation) leads to Erholsamkeit (relaxation).
entspannt - relaxed (calming down, less tension) erholsam - relaxed (recovering from being worn down)
- Both words are related to each other.
- Translation programs will define them both with the word "relax".
- One leads to the other.
- They are the same, but different too.