Facebook reaction 'Thankful' (as 'grateful')

For Mother's Day, Facebook added a temporary reaction called 'Thankful' which was used to mean 'grateful'. This seemed odd. While I am not a native speaker, I was curious enough to use Google. What I found was the following.

'We use grateful to talk about how we feel when someone is kind to us or does us a favour'. [---] 'We usually use thankful when we are relieved that something unpleasant or dangerous didn’t happen'. Cambridge Dictionary

Nevertheless, many dictionaries give them as synonymous with one another.

Is there an important difference which everyone agrees on?

First, the Cambridge Dictionary definition for thankful that you quote is correct, but not complete. Merriam Webster defines thankful as

glad that something has happened or not happened, that something or someone exists

According to this definition, Facebook's use of thankful on Mother's Day makes sense.

Moving on to your question

Is there an important difference [between thankful and grateful] which everyone agrees on

Etymoline explains a difference, and, as a native English speaker its explanation makes sense to me. Whether "everyone" would agree, I can't say.

grateful: 1550s, "pleasing to the mind," also "full of gratitude, disposed to repay favors bestowed," from obsolete adjective grate "agreeable, pleasant," from Latin gratus "pleasing" ......... Grateful often expresses the feeling and the readiness to manifest the feeling by acts, even a long time after the rendering of the favor; thankful refers rather to the immediate acknowledgment of the favor by words. [Century Dictionary] (emphasis added)

Going back to the Mother's Day example: You are thankful that you have a loving mother, but you are grateful that she gave you an interest-free loan to start your business, and you are cutting all your discretionary expenses so as to repay her as soon as you can.