I ran an Email Send program that has a Smart Campaign where Smart List is anyone who "Clicks Link in Email" and Flow is "Change Program Success" to Influenced resulting in 2050 Members with a status of "Influenced". In the Summary section of the program dashboard it shows 10,546 Opens. I then made a Smart List with the filters "Member of Program" with status of "Influenced" AND also "Opened Email" of that program/email which showed 830.
SO, if there are 2050 members with status of "Influenced" (because they clicked a link in that email) how can there only be 830 that opened the email? While the dashboard shows 10,546 opens...
I just want to know who is the most interested in our email which is why I set the "Change Program Success" flow step to anyone that "Clicks Link in Email" so their member status would change to "Influenced"
Opened Email is not a superset of Clicked Email. It's perfectly possible for a lead without images enabled to click a link, so only the Clicked Email would appear in their Activity Log.
In addition you should be aware that not every click is a real human interaction. Mail scanners will pre-click your links to check for malware/phishing sites.
In the Docs it sounded like any clicks will then be counted as opened in an Email Performance Report. See the "Rule" bullet points on Email Performance Report - Marketo Docs - Product Documentation I'd assume this logic works for activity filters too. Have you seen otherwise?
The behavior is absolutely different in these two cases (this has long been known).
There are no implicit activities in the Activity Log.
The EPR uses the concept of an implicit open when computing statistics.
Perhaps it would be worth double-checking that the filters were all referencing the correct email assets?
Were you wanting to measure how many people were either "influenced" (clicked) or "opened email"? You'd want to make sure you're using the ANY rather than ALL in the smart list. The way you're describing it the person had to have done both, which is why it wouldn't match the 10,546.