External Audio Recorder - Recording and mastering your audio separately and externally will almost always give you the highest quality results, provided you feel confident with your recording device and settings.
Different audio scenarios will require different types of microphones, settings, proximity and placement, however a standard XY stereo recorder is a good base for recording the overall ambient sound of a scene.
There are a number of XY microphone adapters available for phones also, which could be used to turn a 2nd phone into the audio recorder for a scene.
XY Mic - Stereo / Full Sound / Music / Environment
Shotgun Mic - Directional / Targeted / What you're pointing at / Excludes handling noise
Shotgun Mic - Shotgun microphones are directional mics which focus on a sound source directly in front, attempting to minimise environmental sounds around your subject. They can work for dialogue, but also for any audio activity your subject may be undertaking in addition, such as dancing or playing an instrument. The sound of the room, or the sound of your hands operating your camera will not interfere as much as for other types of microphone.
If you are lucky to still have a 3.5mm headphone jack on your smartphone, then you have a wider range of microphone options, and can often adapt pro video mics with simple trs to trrs adapter cables.
Newer apple devices require mics specifically designed for the lightning port. Fortunately there are a lot of options available. Rode in particular make a few good options such as the Videomic Me-L.
Lavalier Mic (Lav) - Lavalier microphones are discreet mics which are pinned to or hidden underneath your subject's clothing in order to be as close to your audio source as possible, thereby minimising external noise interference.
An external recorder or 2nd phone is often needed, unless you have a very long cable, extenders can often be purchased.
Lavalier mics work best for dialogue and will provide the greatest clarity, in a variety of environments, for the voice of your subject.
Lavelier Mic (Lav) - Voice / Close to the body / Discreet placement
Wireless Mic - Transmits audio signal direct to the device / Sometimes records
Wireless Mic - Wireless mic solutions such as the Rode Videomic Go can be used on smartphones with the 3.5mm jack and a trs to trrs adapter.
They allow for the close proximity of a lavalier, without the need for long cables to your device meaning your movement can be more free. Useful for people who want to demonstrate movement such as dance instructors, or during presentations where speakers can be free to move around the space.
Boom set up / Blimp - This set up involves suspending a long pole above the heads of the subjects to capture the voices, natural movement sounds, etc. The boom pole allows the microphone gets as close to the action as possible whilst keeping it out of shot.
Boom poles are usually operated by dedicated audio technicians, which helps to keep the set up movable to follow the action of the subject, but also so they can monitor levels using headphones and can make gain adjustments as needed.
They can also be fixed to dedicated microphone stands in static set ups such as interviews.
The microphone is usually connected to an external recording device via long cables, or it can be connected to a wireless transmitter.
Microphones are often, but not always, contained within a Blimp which provide wind protection and suspension to minimise handling noise.
Boom set up / Blimp - Allows microphones to be held close to the performers, but out of the shot / Usually needs separate sound operator
Vocal Microphone - For spoken word or music
Vocal Microphone - Vocal microphones are used to capture high quality rich vocal sounds.
They are designed to be placed or held close to the mouth to obtain the best quality sound.
Unlike a lavalier microphone, they are larger in size and therefor more visably present making them less suitable for a lot of video set ups.
They can be used for musical set ups where we expect to see these types of microphones, and for some on-the-go interview situations where there isn't the opportunity to mic someone up with a lav.
They can also be used off screen to record music or vocals such as narration or voiceover.