The Patek Philippe ref. 5208 is a Minute Repeater Perpetual Calendar Chronograph. It was introduced at BaselWorld 2010 and features an instantaneous jumping perpetual calendar, a minute repeater and a column wheel-operated chronograph with a single pusher for the start/stop/reset functions.
The ref. 5308 is a Minute Repeater Split-Seconds Chronograph Perpetual Calendar. It's an updated take on the ref. 5208, with split-seconds chronograph in addition to the minute repeater and instantaneous perpetual calendar. It was introduced during the 2023 Tokyo Patek Philippe exhibition.
The latest iteration, the 5308G-001 was introduced last April at Watches & Wonders.
Best, Emmanuel
A/ REFERENCE 5208
42 x 15.7 mm case & caliber R CH 27 PS QI
1/ Ref. 5208T-010 (Titanium - Only Watch 2017)

credit: @vuonglan.frodos (1-3), @miketay (4) & @alexanderfriedman (5)
2/ Ref. 5208P-001 (Platinum - 2010)

credit: @wpmiami
3/ Ref. 5208R-001 (Rose gold - 2018)

credit: @tony_traina & @tourbillon001
B/ REFERENCE 5308
42 X 17.71 mm & caliber R CHR 27 PS QI
1/ Ref. 5308P-010 (Platinum - 2023 - limited to 15 pieces)

credit: @masayuki6969
2/ Ref. 5308G-001 (White Gold - 2025)

credit: watch-critics (1), @tiempoderelojes (2-3), @chronotempus (4-5) & watch collecting lifestyle (6-7)