I bought a short sale and gave them 30 days to vacate the property. What if they continue to stay? There is no agreement other than the terms on the sale of the home.
Should I start the evication process? Are they considered squatters if they saty after the 30 days?

You can take the tenant to court after you provide them with written notice of non renewal of their Lease. If there is not a written lease, that would imply a 30 day or month to month lease. After written notice of non renewal and the tenant does not move you can take them to court and the court will rule whether the tenannt can be evicted. If the court rules in the owner / Landlord's favor, the owner must then file for sheriff to remove the tenannt, the sheriff will go to the house and remove the tenant.

1. squatters ? So what exactly is that ?

2. they are unpaying renters and you will have to evict them and hope they don't take the plumbing with them, hope they don't leave holes in the walls and more.

This is actually a different situation and I'm not sure if eviction is the right process. It is not uncommon to allow the previous owners to stay in the house for a short time after closing. Generally this is agreed upon in writing at the closing.

I would consult with the attorney that handled the sale for you or a local Real Estate law specialist (Note: ANY question on law needs to include your general locale as laws vary by area). There might be another avenue here since they will become trespassers when the 30 days expire.