This website suggests the version with 'get' is more informal:

https://www.perfect-english-grammar.com/causa...

Have + object + past participle (have something done)

We usually use 'have something done' when we are talking about paying someone to do something for us. It's often used for services. The form is 'subject + have + object + past participle'.

• I had my car washed.
• John will have his house painted.

Get + object + past participle (get something done)

We can also use 'subject + get + object + past participle'. This has the same meaning as 'have', but is less formal.

• The students get their essays checked.
• I'll get my hair cut next week.
• He got his washing machine fixed.