It's a little subtler than that: peers don't just influence to do things, they influence you to want things.
Peer pressure is overweight friends subtly trying to prevent you from losing weight because it makes them feel more bad about their weight. Peer pressure is friends convincing you some trip or experience will be worth it and you should come with them. I don't think of peer pressure as keeping up with the Joneses (but you are right that we already have a phrase for this phenomenon).
"Peer pressure is the direct or indirect influence on people of peers, members of social groups with similar interests, experience, or social status. Members of a peer group are more likely to influence a person's beliefs and behavior. A group or individual may be encouraged and want to follow their peers by changing their attitudes, values or behaviors to conform to those of the influencing group or individual"
I think that keeping up with the jones very much fits into that.
This is a frequent topic of stress in my life. It's almost every other week, my cousin and his family show up at our home and make it a point to rub their latest purchase in our faces.
Some times my wife and mom even fall for it.
My typical approach is to let a week to a month pass between such an incident and for most purchases you realise you don't need it. Eventually you do come across a few things which they buy, and could improve your life and it make sense buying them. But giving a wait period generally helps to see if that is the case.
I also feel bad for my cousin that his happiness depends on staying in debt forever buying things just to show off.