Equivalence of LACP and EtherChannel

PAgP is ciscos version LAGP is the IEEE standard version.

Actually, it's the converse. Cisco's had the technology first, but considered it proprietary (so it required Cisco hardware). So, industry/IEEE seeing a "good thing" created their own "standard" variant. (Cisco has a lot of "first" proprietary technologies that a later industry/standard variant was defined to provide something similar.)

EtherChannel links formed when two or more links budled together for the purposes of aggregating available bandwidth and providing a measure of physical redundancy.

Standards-based negotiation protocol, known as IEEE 802.1ax Link Aggregation Control Protocol, is simply a way to dynamically build an EtherChannel.

Essentially, the “active” end of the LACP group sends out special frames advertising the ability and desire to form an EtherChannel.

Once these frames are exchanged, and if the ports on both side agree that they support the requirements, LACP will form an EtherChannel.

An EtherChannel can be established using one of three mechanisms: PAgP - Cisco’s proprietary negotiation protocol LACP (IEEE 802.3ad) – Standards-based negotiation protocol Static Persistence (“On”) – No negotiation protocol is used.

That leaves LACP and “on“, both of which have a specific benefit.

LACP helps protect against switching loops caused by misconfiguration; when enabled, an EtherChannel will only be formed after successful negotiation between its two ends.

To configure an EtherChannel using LACP negotiation, each side must be set to either active or passive; only interfaces configured in active mode will attempt to negotiate an EtherChannel.

PAgP/LACP is just a protocol to form the etherchannel link.

You can have etherchannel without protocol, but not advisable.