Wikipedia Defines Advocacy Groups as Such:
"an advocacy group normally aim[s] to influence public-policy and resource allocation decisions within political, economic, and social systems and institutions; it may be motivated from moral, ethical or faith principles or simply to protect an asset of interest. Advocacy can include many activities that a person or organization undertakes including media campaigns, public speaking, commissioning and publishing research or poll or the 'filing of friend of the court briefs'. Lobbying (often by Lobby Groups) is a form of advocacy where a direct approach is made to legislators on an issue which plays a significant role in modern politics.
Policy.Ca - a Canadian site - defines Advocacy Groups as such:
An advocacy group is an organization that attempts to influence public policy without putting up candidates for election (as political parties do). Advocacy groups exist along a spectrum that runs from broadly ideological to extremely issue-specific. An example of a fairly broad ideological advocacy group would be the Canadian Taxpayers Federation, whereas a group such as the Pro-Choice Action Network is largely single-issue. Advocacy groups are quite similar to lobby groups, though they do not engage in direct lobbying of governments (which requires registration as a lobby organization). Instead, advocacy groups pursue their respective causes through a variety of indirect means. Advocacy groups generally speak on behalf of a particular constituency in society, attempting to advance the special interests of that constituency accordingly.
Both say advocacy Groups are similar to Lobby Groups but Policy.Ca makes it clear that Canadian Advocacy Groups cannot directly lobby the government.