Here's how most share scripts work:
If you copy and paste their script, "as is", on to your webpage, they automatically detect and share the URL of the page that they exist on. This is why all your ShareThis buttons on the page are detecting and sharing the "current web page" as you put it.
This is what you need to do:
You need to specify the URL that each button should share inside each button's script. Their API has detailed documentation on this.
Let me know if this helps.