Due to the seemingly consistent inability of many people to understand the broader concept you expressed there I feel the need to spell it out in a bit more detail.

Free speech: the freedom to speak one's mind (this can apply in any context).

Any and all consequences for speaking one's mind are a direct assault on one's freedom of speech in the relevant context, by definition.

The first amendment protects individuals who speak their minds from government imposed consequences for doing so. This is meant to prevent the government from curtailing their freedom to express themselves.

"Freedom of speech, not freedom from consequence" means (in the context of the US) that even if there aren't any governmental consequences for speaking your mind there might still be social ones.

Hypothetical situation: People debate the merits of a non-governmental entity (for example, an employer) placing various restrictions on speech in some context (say, in the work place). Someone comes along and glibly points out that "freedom of speech doesn't mean freedom from consequence". Said commenter has _completely_ missed the point.