In the field of law, the word force has two main meanings: unlawful violence and lawful compulsion. "Forced entry" is an expression falling under the category of unlawful violence; "in force" or "forced sale" would be examples of expressions in the category of lawful compulsion.
When something is said to have been done "by force", it usually implies that it was done by actual or threatened violence ("might"), not necessarily by legal authority ("right"). For example, a person forced against their will to commit an unlawful act they would have not committed if not threatened, would be considered lawful.
"Force of arms" is a special case that can be an example of unlawful violence or lawful compulsion dependent on who is exercising the violence (or threat thereof) and their legal right and/or responsibility to do so.
When one citizen threatens another with a weapon without being in danger from the person he or she is threatening, this would be an example of the unlawful expression of force of arms. The same threat expressed by police officer making a lawful arrest would typically be considered lawful compulsion.
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“Most new things are not good, and die an early death; but those which push themselves forward and by slow degrees force themselves on the attention of mankind are the unconscious productions of human wisdom, and must have honest consideration, and must not be made the subject of unreasoning prejudice.”
—Thomas Brackett Reed (1839–1902)