Both appear in my dictionary (CC loaded by pleco). The first definition reads:
“Form, shape, type, style, pattern”. No examples.
The second reads:
“Form, shape, pattern, morphology”. One example:
The native pleco dictionary (PLC) contains only 形態。
Evidence for the use of 型態：
I also found this question about exactly the same thing in Chinese with a couple of answers I have trouble understanding. The answer I understand best seems to suggest 形態 is applicable to material things，while 型態 is more general. This seems hard to reconcile with my dictionary defining both as shape, but at least agrees with the occurrences of 型態 I provided.