Is Curve P-384 equal to secp384r1?
Yes, they refer to the same curve. I'm not sure why the equations' different, but I believe that's just a transcription error. The 04 in basepoint is just standard way to encode a point in SECG #1. 

EDIT: (Answer extracted from the comments)

In the SECG case:

a = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFC

and

p = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFF

so $a = (p-3) \bmod p$

the Nist version does $x^3 - 3x + b \mod p$, whereas the SECG version does $x^3 + (p-3)x + b \mod p$. Subtracting $3x$ or adding $(p-3)x$ is equal $\bmod p$