Hi Steve,
I am going to repost the images here just for reference:
Starts With Flow:

Contains Flow:

For example, using the previous poster's link and 2 screenshots, using 'Start' they initially had 1,788,992 page views, and in the 'Contains' image it had a higher 22,208,466 page views. So far so good.
Yep... 1,788.992 was the number of Start Page views on domain veniracristo.org (i.e. Visit Hit Depth of 1)
And in the contains flow, the number of views (entry or coming from another internal domain) was 22,208,466
However, for 'Contains' in the far right column the top www.churchofjesuschrist.org entry says 1,610,978 ...but in the 'Start' image the far right column the top www.churchofjesuschrist.org entry also says 1,610,978.
Now, in the Start Flow only the first column is the Hit Depth of 1. the second column, showing the domain of churhofjesuschrist.org shows the number of views to that domain that came directly from veniracristo.org.
In the contains, there is no constraint on Hit Depth... as mentioned before, you will see the full views of veniracristo.org, including the "start pages" as well as when this was the last domain in the journey. However, the far right corner, is still showing the churhofjesuschrist.org that came directly from veniracristo.org...
We don't really know how users are using these two domains, so it's entirely possible that the flow didn't significantly change....
Or, this is a bug in flows (since I have now tested multiple start and contain options in my own data, and all the values match....) So, I think you might have found a problem, lol.
So yes, I agree completely the values should be lower... while there are potential instance where the value could be the same, like looking at network that uses a separate domain for a checkout flow, its unlikely that anyone would every get to the second domain without hitting the main domain first... but in this case, I think you hit the nail on the head!
I definitely think you should raise this with Client Care!
I don't use Flow diagrams much to be honest... I usually find them to be a bit busy for my tastes... I prefer the CJA Journey Canvas, which sadly I don't have access to...