Yes, there's a HUGE difference. PCIe (mini or otherwise) is a narrow serial bus, like USB or firewire. 4-wires per lane.

PCI (-X, -mini, or otherwise) is an old-school parallel bus, with a zillion conductors on the connectors.

So, time to google for a mini-PCIe to PCI-expresscard or mini-PCIe to PCIe slot adapter.

Does your other laptop have an "ExpressCard" (external PCIe) slot?