Looks like (bad) parameter sniffing in action.
Grant Fritchey wrote an excellent chapter of SQL Server MVP Deep Dives Vol. 2
all about parameter sniffing and I strongly suggest buying this book. It's a conference in a book. Worth every penny.
Without seeing your code I can't get into details, but looks like the optimizer takes a different path when executing the statement ad-hoc and in a stored procedure. This is something that can definitely happen when bad parameter sniffing kicks in. As to why updating statistics affects the two plans in a different way, I would separate the two issues:
1) statistics are outdated
2) bad parameter sniffing occurs
The parameter sniffing issue is not caused by outdated statistics: it gets worse with stale statistics, but doesn't go away completely when stats are up to date.
However, the fix is easy for both issues:
For the first one, update your stats.
For the second one, you could use local variables or the OPTIMIZE FOR hint.
Hope this helps
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