heavy_blush:

A blush that has a very deep color or covers a large portion of the face. This can be a sign of embarrassment or humiliation. Contrast with light blush.

blushing_profusely:

When a character appears to be blushing especially hard and/or more widespread than normal. This most often applies to characters blushing an extremely dark and/or saturated red, or with the redness/pinkess of their blush extending to most or all of their face.

I don't feel there being any real difference between the two descriptions. There doesn't seem to be a reason to have two separate tags.

The wiki page for blush only links to heavy_blush and light_blush, but interestingly heavy_blush has fewer tagged posts than blushing_profusely.

I believe blushing_profusely was supposed to be aliased away to heavy_blush, see topic #30998.

The bulk update request #9579 is pending approval.

create alias blushing_profusely (2910) -> heavy_blush (513)
create alias slight_blush (183) -> light_blush (125)
create alias blushy (55) -> blush (992857)
create alias blush_face (95) -> blush (992857)
create implication heavy_blush (513) -> blush (992857) # duplicate of implication #64040
create implication light_blush (125) -> blush (992857)
create implication full-face_blush (103) -> blush (992857)

Reason: Redundant tags and missing implications (from https://e621.net/forum_topics/30998?page=1#forum_post_346583 )