As the title implies , what is the difference between these both concepts? According to my understanding , Agile software process uses increments , where some requirements are first implemented and checked. The same for incremental development.
Agile, Development Process – Difference Between Agile and Incremental Development Process Models
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Honestly, I have doubts about the validity of any claim made in a book which sets Agility and Discipline off against each other. Agile methodologies require much more discipline, in my experience, than other kinds of development.
That is, if you're going to exploit the benefits of Agile processes, you must follow the enabling practices that come with them (see Martin Fowler's Is Design Dead article; he is mostly talking about XP, but it applies to all Agility, in my opinion). That takes a lot of discipline.
But, to answer your question, I think that all truly plan-driven methodologies are variations of Waterfall, such as Spiral, which takes development through multiple levels of prototyping before switching to a Waterfall approach, and Cap Gemini SDM, which is Waterfall with very distinct phases where each ends before another starts.
The Software Life Cycle is any process model that has specification, development, validation and maintenance phases and these can repeat in cycles so it's sort of the structure of the development processes:
Software project management considers the practical limits, risks and deadlines and forms a complete plan for the entire project and the maintenance of its progress.
see Wikipedia for more details about Development and Management
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“Agile” is a set of values. One of these: “we have come to value: […] responding to change over following a plan”. This suggests that waterfall-style development models can be inappropriate. In practice, many agile workflows are incremental, for example Scrum.
While there is significant overlap between “agile” and “iterative” models, there can be also agile non-incremental models or incremental non-agile models.
In particular, agile values are not very prescriptive. An agile team may decide on an incremental or non-incremental workflow depending on what works for them. E.g. for a short project, it can be perfectly agile to not divide the work into increments. There are also many practices in the agile-ish space without clear time increments, for example Kanban (which is more about a flow of tasks than delivery in increments), or continuous delivery.
In contrast, a specific incremental workflow may be imposed on a team even outside an agile setting, e.g. because incremental development allows for better risk management or because the increments have to be integrated into a release train.