GFE of course stands for the girlfriend experience or as I like to call it the "Cheeky Girlfriend". This is where the provider is their most warm, feminine, and welcoming self. The encounter isn't rushed but instead naturally moves from playful banter and conversation to an intimate and romantic encounter. The experience is filled with warmth (bah dum tiss), passion, and enthusiasm. There should be affection and intimate touch.
PSE is the porn star experience which is for the more adventurous. While there can and probably should be some playful banter, this experience is filled with more enthusiasm, desire, and raunchier than the GFE experience. I think of a woman who can channel her inner adult starlet - just pure lust. Someone who has a filthy mouth, isn't afraid of toys, revealing outfits, various positions, things landing on their chest or face, and usually partakes in backdoor activities. This style may also involve more heavy S&M, like hair pulling, slapping, and may be more forceful in nature (consensually of course). Basically, you are seeking to reenact what you may have seen in porn.
There are also twists to GFE, like sensual domination or PSE and BDSM/Kink sessions where the provider is the submissive. Suffice to say, in my personal opinion, regardless of GFE or PSE, protection is always used.