I find the two very confusing as some seem to use them interchangeably and some don't seem to. Wiki says they're both the same "...is often called the standard Brownian motion" it says in the "Wiener Process" page.
I understand $B_t$ a Brownian motion is normally distributed $N(0,t)$. But is the "standard" Brownian motion distributed as $N(0,1)$? The name analogous to the standard normal distribution?