Current is another word we use for tradition. If you are Wiccan you might say you are in the Wiccan or the Gardner current since Gerald Gardner founded Wicca. It’s just a way of looking at magick as a flow of energy. Someone at some point started doing things a certain way making the power flow down that path and we call that a current. They often get numerical names based on some kind of gematria (numerology.) Some organizations are actually combinations of two different currents and will carry both names or numbers.
The 151 Current is mine. It is the one I started. It means that whatever energy you get with the name 151 came from me. Many people can get an initiation with Gabriel for example, but they will all be subtly different based on the individual founder. “But if it’s Gabriel’s energy shouldn’t it all be the same?” you may be asking. Yes, but remember the energy always obeys the user’s intention. So the energy is heavily impacted by the intention of the founder of a current. Think of them as a filter.