To calculate the "active" accounts, I have included any transaction that has been made by an account. This can be a post, upvote, downvote, transfer, sbd conversion, power up, power down or even the creation of the steem account itself.

Here are my calculations for the month of June:

Total active accounts: 89,950
Active curators only: 52,750
Active authors only: 42,124
Active curators and authors: 58,904

Good to see we have almost the same numbers :) The difference is, how to define an "active" account. I have included the creation of an account even if the account won't be used thereafter. If I exclude the 'account creation' I count only 62,532 active users in June. To my surprise. It seems a lot of people sign up without using their account thereafter. I did not expect that. I will exclude those accounts in my calculations from now on.