You are close to that answer however let me add few more tibbits
to OP you have to be aware there is open and enclosed lamp verison and with enclosed lamp verison will use the standard socket while the open verison will have specal concat point socket and it will typically show pink in colour so you can not able get standard enclosed bulb in open rated luminaire socket due it will not lit up.
Also I will give you a head up as well you can not interchange between Pulse and Probe start verison if you install the probe start bulb in pulse start system you will simply destory the interal starting device and the pulse start can able lit it off but go the other way around it will not lit up no matter what.
The 400 watts probe start bulb and ballast still on market but seems like the pluse start is getting super common and what more with pulse start the bulb life somehow last longer than plain jane probe start espcally this is true on horzontal postion .
Wisconsin and Paris France
"Pas de problème, il marche n'est-ce pas?" (No problem, it works doesn't it?)