The talent was the money minted by the Temple
A talent was not "minted", a talent was to great an amount to be put into one coin.
The Shekel was money minted by the government, and that was what was used to pay the government taxes to Rome
Nope. The Sheqel was an oriental coin, used in Canaan, in Babylon (under the name "teqel"), and in Judaea in the time of Jesus. There were Jewish sheqels, but there was no Roman sheqel.
Note the last two letters in the word "shekel". The letters "el" when they fall at the end of any Hebrew word refer to God's name, El.
The Hebrew word transcribed as "el", or more precisely
'el, consist in Hebrew of two letters, an Aleph (the
' in the more precise transcription) and a Lam (the
l, vo course), vowels were not written (there are extra-signs for vowels, invented in the early middle ages). There is no Aleph (א) in sheqel (שקל), so what you notice is a coincident in English and has nothing to do with the original words.
And that's why Jesus responded when asked about the tithe :"Give to God what is God's..." because He knew that it was common practice for the tax collectors to "cook the books" so to speak when collecting the taxes.
In that incidence there was no sheqel involved, but a denarion (δηναριον, a Roman coin, the name survived in the form "Dinar" up to now in some countries). The denarion had the image of the Emperor on it, so it belonged to the Emperor who issued it.
But, was not the Emperor (as any human) the image of God?
Please stop issuing misinformation (out of ignorance, not of bad will, I suppose).