A Hidden Element is an Element that is not displayed in the Axsy Mobile App due to the outcome of a formula on the Visibility tab being evaluated as true. With Hidden Elements, no value is sent back to Salesforce in the Form Response.
Even if the Element is hidden in this way, the value that was set for the Element before it was hidden can be used in formulas for other Elements.
For example, the user could have made choices that originally meant the Element was visible and was given a value, but is then subsequently hidden. Although the Element is now hidden, and will therefore be sent back to Salesforce as empty, its value will still be used for other elements' formula calculations. Please see here for more details: Hidden Elements and Formulas
Please see this article for more information on how visibility conditions can be configured in the Designer: How to Edit Elements – Visibility Conditions
Invisible Elements are Elements that have Invisible selected under their Defaults tab. The 'Invisible' value, though not visible in the Axsy Mobile App, is sent back to Salesforce and is available to view via the Form Response toggles. This means mapped values will be synced back to the relevant Salesforce record.