Over on one of the Tulsa history groups, someone seems to have their undies in a minor wad over the term "Brookside". Seems they take umbrage over the label as there is no particular street named "Brookside" , hence, to them, rendering the handle invalid.
"Brookside" is an area. Peoria is a street. Peoria is the main thoroughfare through Brookside; the main artery and division of the enclave if you will. "Brookside" extends from about 31st Street South to I 44, and includes approximately 6 to 8 blocks on either / both side[s] of Peoria.
If one is navigating towards Brookside, for whatever reason, one will undoubtedly traverse Peoria Avenue. But you are still heading to "Brookside". One could cruise Brookside, or cruise Peoria. Or even cruise 'the Ribbon'. The activity would be the same, in the same area, using the same road. And even if one is on Peoria, if you find yourself between 31st and I44, you are in Brookside.
As for the origin of the name, Nancy over at TulsaGal.net has the explanation.
"Brookside" is a somewhat loosely defined area. Peoria is a particular street, that passes through Brookside for a couple of miles.