Mathematical modelling falls into categories, which are: empirical, simulation, deterministic, and stochastic.

Empirical modelling involves examining data related to the problem with a view of formulating or constructing a mathematical relationship between the variables in the problem using the available data.

Simulation modelling involves the use of technology (apps, computers etc.) to generate a scenario based on a set of rules. These rules arise from an interpretation of how a certain process is supposed to evolve or progress.

Deterministic modelling involves the use of equation or set of equations to model or predict the outcome of an event or the value of a quantity.

Stochastic modelling is usually used in business and marketing and takes deterministic modelling one further step. In stochastic models, randomness and probabilities of events happening are taken into account when the equations are formulated. The reason behind this is the fact that events take place with some probability rather than with certainty. You might find Mr Reddy Maths Blog useful about modelling.