I am using these terms in the following ways:

Immersion (Hawke's short definition)

The degree to which the RPG participant is engrossed in the activity.

This is measurable on Likert-style scales using a wide number of TR/RT assessment tools.

Flow (Hawke's short definition)

An optimal state of immersion that can lead to maximal performance by the participant.

This is trickier to measure, while there are degrees of flow, it is somewhat binary in different areas. The more one experiences each of the areas as "on" versus "off", the more intense the flow experience.

When the participant experiences all aspects as "on", they are most likely in the most productive and maximal performance state possible, with the highest enjoyment levels.

If you aren't familiar with flow, you may know it as "being in the zone" in sports. The main proponent of the flow concept is Mihály Csíkszentmihályi.

The key is to balance challenge, environment, participant abilities, intrinsic motivation, and many other variables, so that the participant has an intense, distinctive experience, and is at their optimal state of performance.

Video Lecture on Flow

Here is a video lecture by Hawke Robinson providing some examples of Flow State experiences in sports and gaming: https://www.youtube.com/watch?v=Dbtma-4qUl8

The core components of Flow Theory, as quoted from a summary on Wikipedia:

"Jeanne Nakamura and Csíkszentmihályi identify the following six factors as encompassing an experience of flow.^[2]

1. Intense and focused concentration on the present moment
2. Merging of action and awareness
3. A loss of reflective self-consciousness
4. A sense of personal control or agency over the situation or activity
5. A distortion of temporal experience, one's subjective experience of time is altered
6. Experience of the activity as intrinsically rewarding, also referred to as autotelic experience

Those aspects can appear independently of each other, but only in combination do they constitute a so-called flow experience. Additionally, psychology writer Kendra Cherry has mentioned three other components that Csíkszentmihályi lists as being a part of the flow experience:^[3]

1. "Immediate feedback"^[3]
2. Feeling that you have the potential to succeed
3. Feeling so engrossed in the experience, that other needs become negligible

Just as with the conditions listed above, these conditions can be independent of one another."

The image below is the most common model used to reflect all the variables that need to be perfectly balanced to get into the ideal flow, hitting that "sweet spot" in the center for maximal flow experience.

Quoting from Wikipedia's summary:

"Flow theory postulates three conditions that have to be met to achieve a flow state:

1. One must be involved in an activity with a clear set of goals and progress. This adds direction and structure to the task.^[14]
2. The task at hand must have clear and immediate feedback. This helps the person negotiate any changing demands and allows them to adjust their performance to maintain the flow state.^[14]
3. One must have a good balance between the perceived challenges of the task at hand and their own perceived skills. One must have confidence in one's ability to complete the task at hand.^[14]

However, it was argued that the antecedent factors of flow are interrelated, as a perceived balance between challenges and skills requires that one knows what he or she has to do (clear goals) and how successful he or she is in doing it (immediate feedback). Thus, a perceived fit of skills and task demands can be identified as the central precondition of flow experiences.^[15]"

Related to role-playing games, I have found a lot of variables can improve the likelihood of participants (including the GM) experiencing Flow more frequently and for longer durations. That is what most of the experiments from 2012 through 2014 were focused on. There are a lot of things that can "take a person out" of flow, or prevent them ever experiencing it. But based on the many leisure experience assessment tools I've used for RPG participants, everything listed for qualifying as flow experience was experienced repeatedly by all participants at one point or another. Sometimes everyone in the group experienced it simultaneously, while more often individuals experience it during key points on their own at different intervals than their fellow participants.