Campaigns may not be visible when viewing statistics in Outbrain based on setup in the UI/the campaigns status. If a campaign is archived it may not show up.
Funnel, however, will always show all your campaigns, including archived ones.

Data for this type of campaign will only be visible in the "Campaign statistics" report.

There are a few possible explanations for this.

First, make sure you are using the same attribution model in Funnel and Outbrain. If your Funnel source says “Conversions attributed to click date”, the same should be true for Outbrain.

Secondly, look at the exact conversion you’re interested in, rather than the total.
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In Funnel, add “Conversion Type” and “Conversion Name” to your data explorer view. Then compare the values for each row to corresponding field in the Outbrain GUI.
The column named “Conversions” in Outbrain does not always show all conversions. If, for example, you have conversions of Outbrain's own types “Lead” or “Sales” other conversions may only be visible under their own names.

Finally, if you are using the Campaign statistics by Publisher report, be aware that the data coming from Outbrain's API for this report type contains sampled data. This means that statistics for this report type will generally contain minor discrepancies, and this is fully expected behavior.