Is there any difference between going hand in hand, and hand in glove?

Hand in glove means that two things go together, fit together, like a hand in a glove. That is, they were made for each other and have a tight fit.

Hand in hand means, side by side, holding hands.

Hand in hand means togetherness, a peaceful walk. Hand in glove refers to a gentleness, a tough thing done, gently.

Hand in hand is a choice to be going forward together.

Hand in glove describes a fit – how well matched two things are.

Hand in hand means to do something together, or that they fit together well as equals, like peanut butter and jelly, eggs and bacon.

Hand in glove means that two things fit together in more of a merging way—a relationship or union.

@trailsillustrated said ‘a tough thing done gently’—I think she means the phrase “handled with kid gloves”—that’s when you treat something or someone gently.

if we say two things/actions go hand in hand it means that they are often or almost always to be either found together, or one following on the heels of the other. Perhaps it’s because they complement each other, or because one of the items or actions tends to cause or facilitate the other one. I guess you could say that the two things have a sort of symbiotic and/or synergistic relationship. We say things can, should or do go hand in hand, meaning they belong together somehow in our minds but not necessarily that one of the things is part and parcel of the other.

Sample sentence:
When trying to instill good values in our children it’s important that our lessons go hand in hand with being a good role model.

When one says things go hand in glove with each other it’s more like a a near seamless fit of two different entities which somehow work together as one. I think it’s a very subtle difference. They never lose their separateness but they seem to work in tandem with each other rather than side by side. It also implies a simultaneous rather than sequential relationship between the items/actions. They are in “bed with each other” so to speak.

Sample sentence:
The right wing Republicans worked hand in glove with the conservative press to push for the repeal of Obamacare.