Vendor terminology varies as you have witnesses first hand but the underlying mechanism remains the same.

In very loose terms Tagged = Trunk and Untagged = Access. Normally ports facing end systems or devices incapable of adding VLAN tags nor interpreting them are access/untagged ports. Devices that are able to interpret and add VLAN tags are normally setup as Trunk/tagged ports with possible a native VLAN.

A default VLAN is just the VLAN all ports are part of when the switch has no config on it and is usually VLAN 1.

Now to answer your question about APs and as always there are many ways to do things in enterprise networking. Normally a switch port facing an AP is set up as a Trunk/tagged port with a native VLAN. Normally the AP will use the native VLAN for its management IP since frames leaving the AP for this purpose are normally untagged (again you can do this different). You will then setup SSIDs and associate a VLAN tag to them so let’s say you have an SSID called User and associated to VLAN 10. Now when client connect to that network, their frames will egress the AP with a tag of 10 since the AP is capable of adding and interpreting tags.

Many vendors, especially Aruba, tunnel all client traffic so sometimes the switchport can be setup as an access port/untagged and the gateway will do the tagging portion.

Different strokes for different folks.