Pressure and stress, to me anyhow - are from different sources...
Pressure tends to come from within - and is relatively healthy.
Stress comes from sources that I cannot control yet still affect me... Server goes down in the middle of the day and I've 250 users who are dead in the water while I wait for the server guys to resolve the issue... That's stress...
That's great that you make that clear delineation.
The fact is though, that many people get stressed by their internal pressure.
Hypothetical example:
Sally wants to lose 100 lbs. She's been obese the majority of her life. After a ton of struggle with losing and gaining, self doubt, limiting beliefs and thought processes, etc, etc.... she decides to put her foot down and succeed no matter what.
She sets goals and established outlines of how she's going to go about obtaining said goals.
Yet, each morning when she wakes up she feels nervous and uneasy. Much like you might when a problem arises causing stress. For Sally, even though she made up her mind to reach her goals, the very process of losing weight stresses her out emotionally.
Now that she's made up her mind... it's do or die time. She either succeeds or she fails. What if she fails? What does that mean to her? What does that mean for her future?
Pressure leads to doubt and doubt leads to limiting questions.
Soon, the same pain that caused her to make up her mind about losing weight causes her to fail. Where the pain originally led to things such as disgust, regret, etc... it now leads to internalized pressure that stresses her or scares her out of living up to the goals she set for herself.
It's seems crazy and illogical... however, I've seen it quite a few times. Sure, it's usually not so cut and dry. It's usually not something you can point a finger at and say, "Sally is stressing herself to the point where she sees pain in moving forward."
The stress from the internalized pressure is usually multifaceted but there's always a foundation of thought patterns that are similar in each case. I say it time and time again but perception and self-talk are awesome forces that break people down time and time again.
In truth, I've experienced very similar patterns that I've corrected. Not with my weight or physique... but other areas. It's all the same.