PAR = Parabolic Aluminized Reflector. BR = Bulged Reflector. 30 means 30 eighths or 3.75" diameter that fits in a 5" diameter recessed fixture.

These terms describe an incandescent halogen lamp where the light is reflected internally for a specific beam spread and called a spot or flood depending on the beam spread angle. BR lamps tend to have wider beam spreads.

PAR bulbs are good for recessed light fixtures because they throw more light and they are shorter due to their flat face and are less visible in a recessed fixture. They also produce a more focused light pattern than the BR lamps so the light appears sharper edged and less diffused for a given beam spread. Light beams get wider and more diffused as ceilings get higher so wide soft beam lamps will not be appropriate for your installation.

LED lamps do not use internal reflectors to focus, aim or increase the intensity of the light source (a little light emitting diode), When these terms are applied to then it only means they are "approximately equivalent" in shape and performance to the incandescent lamps. Such marketing terms should always be treated with skepticism; these are very different kinds of lighting devices.

So, you should select an LED lamp by its shape (PAR or BR), lumen output, color temperature and beam spread. Shorter PAR lamps look much better in recessed lighting (I never use BR or R lamps) but LED color temperature varies by manufacturer and is not a reliable color indicator so you should compare the lamps in a store display if possible AND at home. I prefer the warmer 2700K lamps but some people like the cooler 3000K lamps.

The LED lamp choice is also determined by the fixture. The manufacturer's spec sheet will tell you what lamps are rated for a particular housing and trim kit so it will not exceed the temperature limit which shuts down the fixture until the lamp cools and then turns it on again.

The PAR lamp sizes are 16, 20, 30, and 38. The BR lamp sizes are 20, 30, and 40.

LED's are low voltage devices so a transformer (called a driver) is required. The driver can be built into the top of a recessed light fixture or it can be built into the base of a screw-in "replacement" type LED lamp. These lamps fit into standard incandescent fixture trims and housings if they are rated for them. Since you are asking about lamp sizes it appears you are using incandescent housings and trim kits and installing replacement screw-in type LED lamps.

Most of what you will read about recessed lighting applies to an 8 or 9 ft ceiling height. For your ceiling heights you will need at least a PAR 30 (not a BR) in a 5" fixture with a high lumen output on a dimmer. A 4" fixture would look better but to throw enough light you would need a low-voltage halogen MR16 fixture which has a much stronger and more attractive light than any line-voltage fixture although there are some GU10 lamps that come close but IMO fall short. MR16 fixtures tend to be more expensive than other incandescent fixtures but not necessarily more expansive than LED fixtures. You should always price these things instead of assuming one is more expensive. The MR16 lamps last a very long time but they use more power and are more difficult to replace since they have pins instead of a screw base.

IMO this is not an owner design task; I recommend consulting a good lighting store that provides competent lighting advice even if you must pay a fee for it, in fact, it is best to pay a fee.

I had to buy PAR and BR LED bulbs in 2700K and 3000K temperatures and compare the 4 in my house. The differences were readily visible in my house and my designer and I respectfully disagreed over which one looked best. A good local lighting store may have some loaner bulbs you can test out. I bought the bulbs, kept the boxes and will donate the extras to a local thrift store as if they were electronics.