For Pressure Canning, can I use any other jar than Ball’s Mason Jar?
The important part of the system are the lids. The ideal lids are the Mason-type (no matter which company produced them), with a flat top and a separate side piece with thread. 



Another type that works is the older Weck style jar, which consists of a glass jar with glass lid, plus rubber steal and metal clamps, no threads. This system is as safe as the Mason style lids. It might require frequent rubber replacement when pressure canning, because the gasket gets quite deformed in pressure canning as opposed to water bath canning, and in the extreme cases, some jars don't seal properly because the gasket gets sucked inside. This is not a safety issue, because it is easily recognized when it happens, and you just remove these failed-to-seal jars from your batch. 



What you cannot use is single-piece twist-off LIDS as in your picture. They are not suited for pressure canning at home. 

You might be able to use these jars, if you can find ones with the proper size mouth and threads to fit Mason-style lids on them. They will either seal properly and be safe, or not withstand the pressure and break apart while being heated in the canner. You will lose some jars that way, and will have a mess on your hands to clean, but you will not get food poisoning from improperly sealed jars. See https://www.healthycanning.com/re-using-bottles-from-store-bought-products/ for some expert opinions on that.