TLDR: The Pokemon you find in the wild do not get the Gigantimax form and move that they would get if you caught them in a Max Raid Battle.
Although I'm sure you have already found this, here is a list of all Pokemon that have a unique Gigantimax form/move: https://www.ign.com/wikis/pokemon-sword-shield/List_of_Every_Gigantamax_Pokemon#Gigantamax_Drednaw
I can confirm that Pokemon caught in the wild cannot get the unique Gigantimax move since when I Dynamax my Corviknight that I raised from a Rookidee, it does not get the unique form/move just the default flying Dynamax move.
The real issue with this is the terminology Gigantimax. All Pokemon can become giant and get moves based on the types of their existing moves but not all Pokemon get the unique Gigantimax form or move even if it is the same species as the ones that have the unique form/move. I find it strange that they use the same terminology but that may be a misunderstanding on my part.