Correct spelling, explanation: the words modeling and modelling share the same etymology, and there is no difference in meaning between them. Both forms are derived from the Middle French word modelle, which itself comes from the Italian word modello, meaning a model or mold. The use of modeling with one -l is prevalent in American English while modelling with two -l’s is the preferred spelling in British English. The difference in spelling is mainly a result of the variations that developed as the English language evolved on both sides of the Atlantic.

Definition of modeling:
1. Noun, the act, art, or profession of a person who models
Sarah pursued a career in modeling and quickly became known for her elegant runway presence and striking photo shoots.
As a teenager, Alex dreamed of entering the world of modeling, and after years of hard work, landed a contract with a prestigious fashion agency.
2. Noun, the process of producing a sculptured form with some plastic material, such as clay
The artist spent hours meticulously modeling clay to create a lifelike sculpture of a majestic lion.
In the art studio, students engaged in the process of modeling, shaping their visions into tangible forms through the use of various sculpting techniques.

Collocations with modeling:
Some of the most commonly used collocations include:
1. Role modeling: serving as an example or inspiration for others through one’s behavior.
She became a role model for young entrepreneurs, demonstrating resilience and success in the business world.
2. 3D modeling: creating three-dimensional representations of objects or scenes using computer software.
The architect used advanced 3D modeling techniques to visualize the building before construction began.
3. Life modeling: posing for artists or photographers to be depicted in various art forms.
The art class hired a professional model for life modeling sessions to practice drawing the human form.

Correct spelling, explanation: the only difference between modeling and modelling is the spelling; they represent the same word and have the same meaning. The distinction lies in the spelling conventions of American English and British English. Modeling is the American English spelling and modelling is the British English spelling. Both forms refer to the process of creating a model or representing something through a model, but the choice between them depends on the variety of English you are using.