The words encyst, insist sound the same but have different meanings and spellings. Why do encyst, insist sound the same even though they are completely different words?
The answer is simple: encyst, insist are homophones of the English language.
To enclose in or as if in a cyst.
To take the form of or become enclosed in a cyst.
To inclose or become inclosed in a cyst or vesicle.
To inclose in a cyst.
To stand or rest; find support: with <em>on</em> or <em>upon.</em>
To be resolute or firm in a demand or course.
To assert or demand (something) firmly or persistently.
To rest, dwell, or dilate earnestly or repeatedly; urge: with <em>on</em> or <em>upon:</em> as, I must <em>insist upon</em> your coming.
Definitions from The American Heritage® Dictionary of the English Language, 5th Edition., from The Century Dictionary., from the GNU version of the Collaborative International Dictionary of English. and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.