What is the difference between Shimano BB71 and BB72 bottom brackets? I often see the Shimano BB71 and BB72 press fit bottom brackets listed on stores alongside one another, like here for example, so what's the difference?

Are they both the same geometrically? Is one a premium version over the other?

Additionally it appears my Giant TCR Advanced 2 2016 has a BB-71, though from an answer below it appears that's an MTB bottom bracket? How does that make sense?
From the very amazon.co.uk page you quoted:


  Hi, what is the difference between these 2 bottom brackets.i have a sm-bb7141 bottom bracket on my giant tcr composite 1 2013,not which 1 to buy
  
  Answer:
  The SMBB7241B comes with the 86mm sleeve interconnecting the bearing cups - this is suitable for BB86. The XT SMBB7141A has a 93mm sleeve suitable for MTB frames - I'm not entirely sure which standard this is.
  By Chris Gold on 13 February 2018 


So, at least the width of the sleeve is different, and one is marketed for road bikes (hence the Ultegra branding), while another one is for MTB (hence the XT sticker).