Are you training? I highly encourage you to check out The Four Pillars of Singing, or it's smaller counterpart on Udemy.
Singing and speaking are very different configurations of the musculature being used. Singing tends to be lifted away from the throat and more soft and hard palate focused. Registers and bridges/passaggi are also a bit different, although most people refer to their bridge as a switch in registers.
The Short Answer
Your registers are, from low to high pitch: Pulse, Chest, Head, Whistle. With the ability to mix the chest and head voice together in varying degrees. The most talked about bridge is the one right at the threshold of chest and head voice. However, a bridge is simply a shift in resonance and vocal tract shape to help support singing the next set of pitches. You have multiple bridges within head voice.
The Long Answer
The main vocal registers most often talked about are chest and head voice. Chest feels similar to speaking resonance. Head feels more between the ears and often sounds like mickey mouse. Mixed is not it's own register, rather singing in the head voice range with chest voice musculature mixed in and therefore chest resonance as well (from more surface area in the vocal cords). Falsetto is often mistakingly used as a simile for head voice, when it's actually an open and airy muscle configuration usually within the head voice range. Pulse is below the chest voice, caused from the vocal folds being too loose to do much else.Whistle is above head voice, caused by the glottis/vocal-folds being too closed to do much else but whistle.
The passaggi, or bridges, are shifts in pressure and resonance between various formants in order to support a range of pitches. You have several formants or "resonance chambers" that you're working with. In short, Formant #1 resonates more in the throat ("chesty"); Formant #2 more in the front of the mouth or "mask" ("tinny/brassy"); Formant #3 more in the soft palate ("heady/floaty/rounded"). There are more, but I'm trying to keep it simplified.
The main bridges are around E4, A4, D#5, and A#5. For Females, leave off the E4.
What you're feeling around G3 is a limit to your speaking voice. When shaped for singing instead, you won't feel that limitation until D4 or E4. And if training, you'll be able to smoothly bridge between registers, whether staying connected to your chest voice resonance or not (it will be your choice how much). What you're feeling at the F#4 and G#4 are definitely shifts in formants, but still from a speaking voice configuration rather than a singing one.
Besides getting start through one of the links I placed above, try this:
Place a finger on your bottom lip, and try to sing up and over it. This will help introduce you to the feeling of lifting the resonance out of the throat and to the palates.
Cry/whimper like a puppy, top-down at the back of the soft palate while you sing. There are far too many benefits to list here, but basically this makes it much easier to sing.
Touch your tongue to your upper molars and smile while you sing. This greatly help you to stay "up and out" with your voice.
Start humming while buzzing your lips as much as you can stand it. This balances compression and air support, helps you get used to "up and out" resonance, and is a good beginning for training your singing musculature.
Once you do the above, start working on bridging and connecting your voice. While you can look up Robert Lunte's YouTube videos on cry and bridging, the above courses will do FAR more for you.