How to get from Jerusalem to Ben Gurion airport on Saturday?

Nesher Tours is the operator licensed by the Israeli Airport Authority to operate shuttles to Jerusalem, they operate 24 hours a day, 7 days a week (except for Yom Kippur). On their site they have two different services:

• Taxi to BGA: costs 64 NIS for pickup from anywhere, or less for pickup from their station.

• Suttle to BGA: costs 61.9 NIS, picks up from anywhere.

I couldn't understand from the site what is the difference between the two services. In either case, you need to call them to coordinate, their phone number is 02-6257227 (or 072-264-6059, 1599-500-205).

According to the Israel Airport Authority:

Nesher shuttle to Jerusalem and the surrounding regions depart from the service post on Level G, next to Gates 01-03. There are signs directing to the post. The service operates 24 hours a day. Telephone: 02-6257227 Fees: Service fee to passenger's address: Mevaseret Zion, Ma'ale? Hahamisha, Beit Zait, Abu Gosh, Kiryat Anavim, Shoresh, Beit Meir, Shoeva, Beit Nekofa?, Harel Interchange 64 NIS (about $21 US) Central Jerusalem 69 NIS (about $23 US) Ma'ale Adumim 55 (about $15 US)

A Taxi service like Bar Ilan (private Taxi) costs 200 NIS (about $67 US). They do not operate on Saturday day (but you will be able to order a taxi from 8pm until about 2:30 am on Saturday Night). Taxi Drivers should be available at the terminal listed above and you can order a taxi via the IAA to make sure you're not ripped off.