That's indeed the case.
Now, we use the same piece of code for both the user account email and the order creation email.
The only difference is the content of the email.
I suppose your mail server might be rejecting some emails because of a strange configuration.
You could try to change the settings one by one under the emails tab of the configuration of HikaShop and test if it works after each change.
For example, I know some servers do not accept emails when the name is added so we have an option to turn off this feature. Other servers do not accept emails with too long lines (the order creation email has lines longer than the user creation email so it could be something to look at here) so we added a "word wrap" option. Etc...
All in all, this problem doesn't come from HikaShop as it's able to send the account creation email. Plus, all our other users are able to send the order creation email too. If you cannot figure it out, you should really ask your hosting company what could be the problem.