Both innovation and continuous improvement are the way to adapt to the changes; either step-wise, or breakthrough.
Innovation is the larger umbrella term that encompasses continuous improvement, innovation is also expanding its horizon, goes beyond products/services innovation, it could mean business model/process /culture/leadership innovation, as well. They are either the same or different in many ways.
Linear vs. Nonlinear process: Continuous improvement is a linear process pointed at creating stable processes. Innovation is a nonlinear process involving non-stable processes; continuous improvement expresses a stepwise process toward something "better", where the objective of the improvement can be anything and "better" can have just an internal meaning while innovation stands more for a project type of activity where the reference point could be business eco-system.
Different twist vs. Old fashion way: An innovation is when you change the game; you bring a different twist to what is currently established and perceived. Continuous improvement is by tweaks of things in the old fashion way to bring efficiency. But, even a very small improvement leveraging a new way of doing things, bringing an outside method, or view, shifting the paradigm, is innovation. Innovation breakthroughs that really hit the spot are nearly always 1) respond to a true human need, 2) ride on emerging trends 3) simplify business models and 4) combine all the firm’s capabilities in a unique way to a) wow customers and b) build entry barriers.
Specialty vs. Transdisciplinary: Continuous improvement takes specialty; while innovation is trans-disciplinary. Continuous improvement = technical specialists making the product/service more efficient, up-to-date to the consumer needs. Innovation happens when a non-specialist question challenges the rules of the game, inventing knowledge transfers and goes outside the industry to invent a radical new way to respond to the 'job to be done.' It can also be categorized into (1) Intersection innovation, that is, ideas that result from the clash of consumers and producers are more likely to be out of the box and disruptive, more readily identifiable as innovation. (2). Directional innovation, that results from either the producer or consumer are more likely to resemble continuous improvement.
Improvement-Innovation is a continuum: Innovation can be defined as a continuum, with smaller improvements being closer to one edge (the incremental one) and radical changes being the other edge. In any case, the "newness" of any change in question is relative and depends on which dimension of change one chooses. Continuous Improvement - you take a base and build upon it. Innovation - You build off of an entirely new base. Also, in innovation, you find new ways to expand the market to beyond the people already involve.
Incremental Innovation vs. Radical Innovation: It may be easy to split the term "innovation" into two categories, "incremental innovation" and "radical innovation." Incremental innovation has equal notion/concept with continuous improvement, focusing on improving a part of business process. Radical innovation focuses to "replace" conventional value stream with a new one, supported/filled with noble knowledge and idea. “If at first, an idea is not absurd, there is no hope for it.” Einstein was obviously holding out for disruptive change.
The scope, scale, and impact of the changes: The broader the scope, scale, and impact of the change, the more one leans towards calling such change an innovation. Some additional variables that might merit consideration are the scope, scale, and impact of the change(s). Two key factors, are i) impact on the corporation and ii) whether there is increased revenue generation, either from expanding existing markets or creating entirely new markets. The very successful organizations must manage a portfolio of initiatives, prioritized with adequate support, across the whole spectrum - make the current business better; look for new business and everything in between.
Innovation is "a change that adds stakeholder value." Now if your stakeholders are internal process owners and your output stakeholders are the same, the type of innovation you have is Continuous Innovation. If you take knowledge from one context and bring it over into a new context you have knowledge or technology transfer innovation. With continuous process improvements, you often reduced costs and increased productivity *without* increased revenue generation. On the other hand, if the change, whether an improvement on an existing process or the addition of an entirely new process, leads to increased revenue generation, either from the expansion of an existing market or the creation of a new market, then it’s more as innovation.
The purpose of differentiation is not about separating and siloing these changes but how to best link them together - across focusing on core activities and through continuous improvement, new product development, and innovation - having a suit of tools and people to help realize the change you have defined. Innovation needs to be introduced all over the spectrum of the product life cycle (refreshing the portfolio, finding totally new fields or ensuring on-going profitability and extension of the current portfolio), and an organization must also seek continuous improvements all the time, with a combination of introducing tweaks and innovations.