I have often stumbled when trying to explain the differences and the relationship between Etherchannel, LACP, and IEEE802.3ad. I began stumbling more when I learned that vSphere 5.5 supports Enhanced LACP and LAGs. Here is may best attempt to clarify.
Etherchannel: an Etherchannel is a logical channel formed by bundling together two more links to aggregate bandwidth and provide redundancy. Another acceptable name for Etherchannel (an IOS term) is port channel (an NXOS term). Another acceptable name is Link Aggregation Group (LAG)
LACP: a standards based negotiation protocol used to dynamically build an Etherchannel. It is known as the IEEE 802.1ax (or IEEE 802.3ad) Link Aggregation Control Protocol (LACP). It is a protocol used to build Etherchannels (LAGs) dynamically. LAGs (Etherchannels) can be be also be built statically without using LACP.
IEEE 802.1ax: The IEEE working group that defines port channel, EtherChannels and link aggregation. Orinally, the working IEEE group was 802.3ad, but in 2008 it was replaced by 802.1ax.
IEEE 802.3ad: the original IEEE working group for port channel, EtherChannel, and link aggregation. Although it has been replaced with 802.1ax, referring to IEEE 802.3ad is typically acceptable. So references to IEEE 802.3d LACP are common.
vSphere pre version 5.1: the standard virtual switches and distributed virtual switches provided natively by VMware vSphere 5.0 and earlier do not support LACP (dynamic LAG / Etherchannel creation); however, they support statically built LAGs (or this may be called static LAGs or static Etherchannels)
vSphere 5.1: the distributed virtual switches provided natively by VMware vSphere 5.1 support LACP (dynamic LAG / Etherchannel creation). The support is limited to one LAG per ESXi host and per dvSwitch
vSphere 5.5: the distributed virtual switches provided natively by VMware vSphere 5.5 support LACP (dynamic LAG / Etherchannel creation). It supports 64 LAGs per ESXi host and 64 LAGs per dvSwitch.