Is the SSD "stick" in the MacBook Pro the same as the Mac Pro?
The model of MacBook Pro will make a large difference as to whether or not it's compatible with the Mac Pro, assuming you're talking about the "new" 2013 model.

Specifically, the Mid-2015 MacBook Pro will work, but earlier generations use various different interfaces which will not be compatible.

As you can see comparing this photo of a 2012 MacBook Pro's SSD and this photo from the 2013 Mac Pro, the interfaces are completely different. Alternatively, you can see the same pinout in the 2015 MacBook Pro on this page.

I recommend sticking with 3rd-party upgrades provided by OWC (since they will tell you exactly what they've been tested with), or only getting parts that could have shipped with the original machine. (For example, ordering a broken Mac Pro off of eBay that came with a larger SSD that you can extract.)