Never, Never, substitute one type of primer for another. Even with different manufacturers of
primers begin at the starting loads suggested in published reloading manuals.
Small rifle primers should never be substituted for small pistol, and so on. I know it
sucks to wait for a certain primer size & type of primer. It will suck more to destroy your firearm
and or yourself. I’ve been reloading metallic cartridges & shotshell for over 4 decades. Please
pay heed to my advice. By using components other than the correct type, others are deprived.

Rifle primers are generally considerably hotter than pistol primers, and will raise pressure (sometimes to dangerous levels). How much they raise pressure varies with the particular cartridge, primer, powder and load, and isn't really possible to predict in a general way. However, in most cartridges a starting load is likely to be safe with rifle primers, but anything beyond that should be carefully approached. If you have a chronograph, keep velocity within the limit of what loading manuals show with your particular cartridge, powder and bullet, and you should be within the acceptable pressure range (or, at least close). Small rifle and pistol primers are the same height and create no problem there, but large rifle primers are taller than large pistol primers, and can only be used if your primer pockets are deep enough to keep the top of the primer below the level of the case head.

Russell, many are using small rifle primers in place of small pistol primers. SR primers have a harder cup so that when used in a rifle with higher pressure they do not pierce and allow hot escaping gases to damage the bolt face and firing pin. SP primers have a softer cup to make them ignite reliably with handgun firing systems. Many claim there is no difference in intensity of ignition. Cheers and stay safe!

You should be fine with using the small rifle primers the only difference I know of is that the small pistol primers are made of softer metal