Agile and waterfall approaches are very beneficial for project management therefore it is important to know which approach is the most suitable for a project. Here below is a comparison between them in the form of similarities and differences.

Similarities

• Both Agile and Waterfall approaches have similar goals , which are to produce top quality products and to make clients happy and content.
• They have similar frameworks of collecting , designing , developing and testing.
• The foundation of the processes is planning, creating the project and monitoring it utilizing one of these two methods.

Differences

• The timeline is one of the biggest differences between the methods , for instance the waterfall approach has a fixed timeline. The whole concept is that from the beginning the whole project is mapped out (from start to finish). On the other hand the agile approach has a more flexible timeline since it experiments with different directions.
• Another difference is client involvement, both approaches involve their clients differently. For the waterfall approach, when the goal is established they do not involve their customers through the process since they do not need customer feedback. However the Agile approach includes its clients in every project development step.
• The Budget is allocated differently between the two approaches. The Waterfall approach usually has a fixed budget because the project is already planned since the beginning. For the agile approach the Budget is flexible since it is open to adaptation and change of direction is welcome.

For further information please consult:
https://www.edrawsoft.com/agile-vs-waterfall.html
https://www.forbes.com/advisor/business/agile-vs-waterfall-methodology/

General Information
Waterfall project management maps out a project into distinct, sequential phases. The following stage of the project can only begin once the prior stage has been completed. The Waterfall system is the most traditional method for managing a project, with team members working linearly towards a set end goal. Every member has a definite role as the goals and phases of the project do not change.

History
Dr Winston Royce, a Director of Engineering tried to cut costs and make is projects more predictable in the 1960s. In a paper he described the “waterfall” process exactly how we know it nowadays. 

The “waterfall” process became an important process in software development, the basis for stage-gate lifecycles and is used for a lot of financial processes. 

Advantages

• Replication possibilities; this is an advantage as waterfall workflows can be used for other related activities in the future.
• It is easy and simple to use
• Phases do not overlap

Disadvantage

• One disadvantage of Waterfall is that it is quite inflexible as each task involved is planned in a linear sequence. 
• Any change in stakeholder priorities or needs will disrupt the order and require a revision, or possibly an entirely new blueprint. 
• Waterfall project management is not very efficient for knowledge based projects. For example, computer programming.

For further information please consult:
https://www.wrike.com/project-management-guide/faq/what-is-waterfall-project-management/
http://tryqa.com/what-is-waterfall-model-advantages-disadvantages-and-when-to-use-it/#:~:text=space%20shuttles%20etc-,Advantages%20of%20waterfall%20model,Phases%20do%20not%20overlap.
https://www.artemisagile.com/the-history-of-waterfall/

General Information
Agile is a way to manage a project by breaking it up into several phases. It involves constant collaboration with stakeholders and continuous improvement at every stage. Once the work begins, teams cycle through a process of planning, executing, and evaluating. 

With this methodology, demands and solutions evolve through the collaborative effort of self-organizing and cross-functional teams and their customers.

History
In 2000, a group of 17 software developers, including Martin Fowler, Jim Highsmith, Jon Kern, Jeff Sutherland, Ken Schwaber, and Bob Martin met in Oregon to discuss how they could speed up development times in order to bring new software to market faster. They recognized two key opportunities :

• Shortening the delay of benefits to users in order to resolve the product-market fit and development problems
• Getting feedback from users quickly to confirm the usefulness of new software and continue to improve on it accordingly.

At the beginning, “Agile” was applied to software and IT development projects.  However, nowadays it has expanded to other fields, too, especially in the knowledge and services industries.

Advantages

• Encourages reviewing and rewriting steps to achieve desired results 
• Tasks are tested in flight, leading to faster delivery and a better project
• Requires a lot of feedback between teams, clients and customers → collaborative environment in which silo walls are broken down and collective creativity often flourishes
• Frequency of deliveries allows the project direction to change quickly while maintaining the project scope

Disadvantages

• Does not impose a strict timetable, which can be difficult if a tight deadline is not met
• Often requires a quick shift from one aspect of the project to another → little time to properly complete the paperwork at each stage. 
• Changes in project requirements can lead to problems in other areas of the organization 
• Requires a unified team → weak links in the agile team or management can waste time and money

For further information please consult:
https://zenkit.com/en/blog/agile-methodology-an-overview/
https://www.digite.com/agile/agile-methodology/#agile-methodology
https://www.wrike.com/project-management-guide/faq/what-is-agile-methodology-in-project-management/
https://www.workfront.com/project-management/methodologies/agile/agile-vs-waterfall
https://gosuperscript.com/blog/pros-and-cons-of-the-agile-approach/