Your are correct. Most of the missions built successively larger churches. The fifth and final Santa Clara church was built in 1825. It lasted over one hundred years, but burned to the ground in 1926. The present church is a modern interpretation of this 1825 structure.
There is more available in our key facts section of Santa Clara.
A talented artist, Oriana Day, did a wonderful painting of the 1825 mission, which is shown below:
ARTIST DEPICTION OF SANTA CLARA