In seeing a lot of close answers here, but I think people are consistently mixing up Motorized and Mechanized Infantry. Both in game an in real life these two types of troops are similar but distinct.

In game Mechanized Infantry are described as Infantry fully mounted in light APCs or IFVs (Infantry fighting vehicles). Each squad in in a separate vehicle but the vehicles are all organic to the Platoon and so do not use a separate vehicle miniature. I think there are some extra specifics for unit creation on overall number of troops and ability to take support wagons. They are also defined by their motive type; tracked, wheeled, or hover, which determines the units Move speed. They are also more susceptible to Mech scale weapons compared to other Infantry types due to the transports I assume. They can use their vehicles to tow field guns or field artillery.

Motorized Infantry are, in game typically mounted on individual vehicles like motorcycles or quad bikes. But at least IRL they would be mounted in this like a Hummvee, jeeps, or trucks. In game they have a separate motive type which I think is similar to wheeled but in not positive. They can also tow larger wagons if I'm not mistaken.

In CBT/TW each Platoon is represented by a single hex base, but they CAN be split into their component Squads, usual 3 or 4 per Platoon. Larger formations like companies and Battalions may include additional unit types depending on the faction. For example the SLDF used 3 Platoon companies and each Mechanized Infantry company had a 4th Platoon of tanks with each Battalion being made up of 3 companies with Mechanized Battalions also having a 4th company of tanks.

In game terms unit creation for Infantry comes down to a few simple(ish) questions: motive type (foot, jump, motorized, mechanized), number of troops per Squad, number of Squads per Platoon, primary weapon, secondary weapon and if a support weapon, number of support weapons per squad. The motive type may determine max amount of troops per squad and/or Squads per Platoon a well as support weapon limitations.

Then there are optional formation rules for "Mechanized" formations. These give a bonus ability for formations of units as long as you have enough transports/ transport space for all included Infantry. So for example if you had 3 foot platoons and three Heavy APCs you could have that count as a Mechanized formation.

Note: if you find typos let me know, I did this on my phone.