Appmon are  app lifeforms that possess artificial intelligence, thinking and acting independently. In the Real World, they transform into Appmon Chips and are able to materialize via the Appli Drive. (straight from wiki). They are apart of the digimon universe, especially since it is the eight animated series in Digimon and the show is called "Digimon Universe Appli Monsters". Which in Japan started in October 1, 2016.  

Not a lot of info is available currently, will update as information is discovered.

I think it be interesting to see how both compare.

Due to length this will be soley on Digimon.

Digimon appeared with the creation of the internet and are more focused on devices with larger data caches like computers and laptops, but can also move into other devices. According to Digi-Wiki, they appeared on the Internet around 1997. Digimon have several forms of categorization including Levels, attributes, types, and families.
Levels - (official and fanbased)

1. Basic: Baby -> In-training (Baby2) -> Rookie (Child) -> Champion (Adult) -> Ultimate (Perfect) -> Mega (Ultimate)
   
2. Digi-Armor - rookie evolves using a Digi-armor digiegg, power is based on egg and can vary from Champion to Mega. Based on the Digital Elements (Courage, Friendship, ETC...)
   
3. Ideal-Armor - a digimon digivolves further by fusing 2-3 Digi-armor digieggs together. Two can be considered to be about Ultimate and three can be considered Mega. (Based off of DWC group)
   
4. DNA-digivolve - two digimon to combine into one Digimon of a higher level. The two original Digimon consciousnesses join into one, and the combined Digimon can speak with both voices; often simultaneously
1. Warp-DNA: a combination of Warp and DNA digivolution; allows two rookie digimon to digivolve to their Mega DNA form.
5. Warp digivolution - allows a rookie digimon to digivolve straight to Mega Level bypassing or going through the middle forms incredibly quickly.
6. Biomerge - A form of Warp Digivolution; a partner Digimon merges with its human Tamer to rocket to the Mega level. - Other names: (Nexus Fury, ?, ?)
7. Matrix digivolution - A digi-armor digivolved digimon merges with its human Tamer to reach Mega Level (Based off of DWC group)
8. Dark digivolution - A corrupt form of regular Digivolution, usually resulting in an evil digimon. A Digimon dark digivolves when someone coerces it to digivolve forcefully, with a mind clouded with anger, or through dark power. A Digimon digivolved through this method is evil and perceives nothing but its urges to destroy, making it very dangerous.
9. Spirit digivolution - requires the use of a Human to digivolve into a digimon using a Spirit from the Ten Legendary Warriors. Based off of the 10 Natural Digital Elements; Water, Ice, Fire, Electricity, Dark, Light, Earth, Wood, Metal and Wind.
1. Human Spirit - Humanoid Digimon
2. Beast Spirit - Bestial Digimon
3. Fusion Spirit - merging of a Human and Beast spirit of the same element
4. Unified Spirit - A human will spirit digivolve through the use of half the spirits
5. Ancient Spirit - All the humans and spirits merge together to form Susanoomon
10. Mode Change - A Mega level digimon changes to a more powerful form, but remains the same digimon. Other Names: (Burst mode)
11. DigiFuse - Similar to DNA Digivolution, in that it involves multiple Digimon, here known as "DigiXros Units", combining into stronger forms, but also involves attributes of Mode Changing, allowing the Units to rearrange their data and became body-parts or weapons for the new form. The gestalt entity is usually controlled by the Unit with the most powerful soul and mental fortitude. (Double Fusion, Grand Xros, Great Fusion [multiple generals], Grand Fusion, Final Fusion )
1. Dark/Forced DigiFuse - Participants aren't necessarily willing; lead Unit can change if one member's soul overpowers the others.
12. Soul digivolution - (from :IconHawkInAJazzyHat - Allows a Tamer with a partner digimon to digivolve if they're digivice is infused with the essence of 1 or more of the 10 Natural Digital Elements; Water, Ice, Fire, Electricity, Dark, Light, Earth, Wood, Metal and Wind. Data is shared between the Tamer and they're partner, with deep bonds allowing for simultaneous digivolution into Ultimate forms. 

Attributes - Mainly works in a rock, paper, scissors format

• Vaccine - Strong against Virus
  
• Data - Strong against Vaccine
  
• Virus - Strong against Data
  
• Free - Outside the triangle format, is neither strong against or weak against any of the other types
  
• Variable - Typing changes to match it's opponent
  
• Unknown - (extremely dangerous); Typing is superior to all other types, allowing for increased damage across the board
  

Family -These families help determine what attacks Digimon are strong or weak to, as well as influence Digivolution requirements. Help determining a Digimon's element and location.

• Nature Spirit - Consists of members who are generic animal or monster-like Digimon, or those who dwell in desert-like areas. Members of this family are generally of the Earth element, and are weak to the Fire.
  
• Deep Savers - Consists of generally aquatic or polar Digimon, or those who dwell in marine areas. Members of this family are generally of the Water element, and are weak to the Metal.
  
• Nightmare Soldiers - Consists of generally demonic or undead Digimon, or those who dwell in haunted areas. Members of this family are generally of the Dark element, and are weak to the Light.
  
• Wind Guardians - Consists of generally avian or flying Digimon, or those who dwell in grassy or lofty areas. Members of this family are generally of the Wind element, and are weak to the Electricity.
  
• Metal Empire - Consists of generally mechanical or mutated Digimon, or those who dwell in urban areas. Members of this family are generally of the Metal element, and are weak to the Water.
  
• Virus Busters -Are generally sacred or angelic Digimon, or those who dwell in holy areas. Members of this family are generally of the Light element, and are weak to the Dark element.
  
• Dragon's Roar - Generally draconic Digimon, or those who dwell in volcanic areas. Members of this family are generally of the Fire element, and are weak to the Earth.
  
• Jungle Troopers - Are generally insectoid or vegetation Digimon, or those who dwell in tropical areas. Members of this field are generally of the Thunder element, and are weak to the Wind.
  
• None - Are either baby Digimon too young to have families, such as In-Training Digimon, or are otherwise unclassifiable. Also can include digimon of the Ice Element.
  

So, after some thought, I'm redrawing my main digimon Blazermon. As I've only drawn him once for TDC audition. After redrawing his baby, in-training, and finally rookie form; i decided to go back to working on his armor digivolutions.

I had recently recreated his digimental/digi-egg armor of courage, Gorgdramon. The original Tonatiuhmon , is being repurposed and eventually redrawn as a Matrix digivolution coined by  . Its a mega level digivolution by merging an armor digivolved digimon with its human partner. (If matrix digivolution is used, it belongs to  , so give her credit or we're all dead.)

I have the ideas for Sincerity/Purity, Love, and Kindness done. The only thing I haven't done is the Digimental of Light.
As stated via the official wiki, "Most of the digivolutions which occur through this egg have something to do with mythological creatures or fish, and they may also have the Crest of Light somewhere on their body."

Not sure where the fish thing comes from, but focusing on the mythological creatures I've picked two candidates for Blazermon's Light Digi-Armor.

1) Xiuhmon - from Xiuhcoatl, an aztec fire-serpent or turquoise serpent. It embodies the dry season.
2) Zirnimon - from Zirnitra, a wendish (slavic) dragon god of sorcery. It means magically empowered.

I'm unsure which to choose and could use your input. Thank you for the feedback.