Do you store data entered in our forms or pass them through to salesforce?

Regarding FormTitan forms in general
When you create a form with FormTitan and collect data through it - the information is sent to you via email. It is also stored for you by default, allowing you to enter your "Submissions page" for data management like: viewing, editing, deleting, filtering, exporting etc.
If you are set against the idea of storing the data with us you can  choose to cancel this by turning on the "Don't save the data" checkbox. (in Form > Settings > Optimization). from that point on all data entered in the form will act as always, apart from the data - which will not be saved to your submissions page and will not be retrievable.

As for FormTitan forms with Salesforce integration
When you integrate your forms with Salesforce (to write data in SF objects) then the information will be stored in the relevant  in the fields and objects according to your configuration. 
If you decide to turn on the "Don't save the data" checkbox (from the previous passage) - the data in the form will still flow and update your Salesforce objects as usual.

Custom Buttons to store only in Salesforce
In most Salesforce forms the data is entered and when it is submitted - it is saved in your data management page as well as pushed to Salesforce. But, if you wish to update your Salesforce account without the filler submitting the form (and without storing the data with us) - this can also be easily achieved using Custom Buttons.
Read all about using a custom action button to push data to Salesforce.