Hi ... I finally googled images for the Brown recluse spider and the Daddy Longlegs ... the Brown Recluse seems to have a fatter different body and shorter legs than the Daddy.
The whole reason I brought this up was because I sanpped that pic of the spider in my bathtub at the motel while there ... a friend saw the pic of it and said it looked like a Brown Recluse, said, if so, it was dangerous and I should be careful.
If you Google images for the Brown Recluse spider (which apparently likes damp climates) it will pop up a lot of very nasty looking images of what those little creepy crawlies can do to you if you get bit

Quite horrible to look at!
My spider is a Daddy-LL ... it HAS to be, because I insist!