Rifled slugs, in common terminology, are the older Forster ( Usually misspelled Foster) style.
Brenekkes are solid chunks of lead with a separate wad permanently attached.
Forster style slugs are capable of squeezing down considerably and can be shot through most any shotgun and choke.
Brenekkes should NOT be fired through some older double guns but many are safe with them.
Your H&R should be fine with Rifled slugs but they do kick a good bit.