Osaka Amazing Pass / Osaka Unlimited Pass

Is Osaka Amazing Pass same with Osaka Limited Pass?
Can I use Osaka Amazing Pass (1 day) to take train from Kansai Airport to Osaka City?

Osaka Unlimited Pass was renamed as Osaka Amazing Pass from the 2014 Spring-Summer version.
http://www.osaka-info.jp/osp/en/index.html

Can I use Osaka Amazing Pass (1 day) to take train from Kansai Airport to Osaka City?

Which place in Osaka City would you head to first?

An Osaka area edition of 1-day Osaka Amazing Pass (2300 yen) does not cover railroad accesses from Kansai-airport Station.
With a Nankai-Kanku edition of 1-day Osaka Amazing Pass (2900 yen) you logically can travel by Nankai Electric Railway from Kansai-airport Station to Namba Station; if you take a Nankai Limited Express Rapi:t Beta, the additional charge (510 yen for this section) is not covered by this pass.

Anyway, it seems not easy to make a 1-day Osaka Amazing Pass pay off on the day of your arrival to KIX by an international flight, unless you arrive early in the day and use coupons efficiently for certain facilities.

Depending on the places and facilities which you visit and the area where you stay overnight, a combination of
either a Kanku Tokuwari Rapi:t Ticket (1130 yen) of Nankai
or a ticket (1030 yen) included in an ICOCA & Haruka package of JR-West
+ a One-day Enjoy Eco Card (800 or 600 yen)
may be better in terms of saving a cost.
http://www.howto-osaka.com.e.iv.hp.transer.com/top/ticket/railway/toku...
http://www.westjr.co.jp/global/en/travel-information/pass/icoca-haruka...
http://www.kotsu.city.osaka.lg.jp/library/img/english/ticket/obj_con02...