They share a meaning.
lots of – a lot of /loads of– a load of = a large amount, much; a large number, many  (You might also see tons of/ a ton of.)
They are all informal.
many, numerous, countless, a considerable number/amount, much, several, some – more appropriate possibilities for formal contexts
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Both have other meanings.
load –  amount or weight of something carried
The trucks were carrying loads of construction materials.
lot – a set of things
I bid on several lots of vintage postcards on Ebay.  (a lot = one set/collection of vintage postcards)