I was broken - broken is adjective (Be pattern)
I was broken - broken is -en form of the verb (passive form of break)
1) Firstly, do both sentences have the same meaning? and
2) Is my understanding correct to write and explain my question this way?
Since I don't know what literal or figurative meaning you have in mind with "I" as the subject, I'd like to change "I" to "it" before answering your question:
(a) It was broken. (copulative; "broken" is an adjective)
(b) It was broken. (passive; "broken" is a past participle)
Let's suppose "it" refers to a vase. If the vase lay shattered on the table, we may say (a), describing the past state of the vase. The sentence is adjectival.
The passive sentence is quite different in meaning. We could add an agent "by"-phrase and a time adverbial to bring out the difference:
(b1-passive) The vase was broken by John at 10:23 a.m.
That sentence does not describe the past state of the vase, but rather a punctual event in which the vase went from being unbroken to being broken -- cf.:
(b1-active) John broke the vase at 10:23 a.m.