SAVR = Surgical aortic valve replacement This is open heart...

SAVR = Surgical aortic valve replacement
This is open heart surgery. The patient has their chest opened. Surgeon has clear view and can perform operation by hand.

TAVR = Transcatheter aortic valve replacement
This is to avoid open heart surgery, particularly in the case of the elderly that may not tolerate major surgery. In a 'keyhole' type procedure, the surgeon accesses the faulty valve via a long catheter, inserted into one of the larger arteries (typically the femoral artery at the groin, but access via subclavian artery in the chest is possible also). Surgeon performs the surgery using video feed and micro-manipulators.

Because TAVR is usually reserved for high-risk individuals, you'll find the mortality rate is higher than for SAVR. Nonetheless, improvements to TAVR could see the procedure be used in favour of SAVR.

Hope that makes some sense. Here is an enthusiastic powerpoint from 2014;
https://www.ucdmc.ucdavis.edu/inter...ium 2014/Kori and Janine TAVR Debate 2014.pdf