history vs past times

history and past times both are nouns.

Word	Noun	Adjective	Verb	Adverb
history	Yes	No	No	No
past times	Yes	No	No	No

As nouns, past times is a hypernym of history; that is, past times is a word with a broader meaning than history:

Other hypernyms of history include past, yesteryear.

history (noun)	past times (noun)
the discipline that records and interprets past events involving human beings	the time that has elapsed
all that is remembered of the past as preserved in writing; a body of knowledge
a record or narrative description of past events
the aggregate of past events
the continuum of events occurring in succession leading from the past to the present and even into the future