Are they linked, or have they arisen seperatedly and/or without connection?
The Oxford English Dictionary indicates that in English -wise branched off from the noun wise, in the sense of "in what wise" (in what manner). The relevant entry under "wise, n.1" describes -wise functioning as a noun qualified by an adjective or another noun, much as we might say red car or diesel car. Over time the compounds became single words or expressions and -wise was interpreted as a suffix. (Imagine if redcar and dieselcar became words and -car were generalized to mean "a vehicular conveyance.") The entry explains:
II. Old English wíse manner, fashion, like the cognate forms in other Germanic languages (see the respective sections below), was used in various kinds of adverbial expressions meaning ‘in such-and-such a manner, way, or respect’, in which it was qualified by an adjective or a noun with or without a governing preposition. Several of these expressions, with others formed on their pattern in later periods, have survived as simple words, e.g. anywise, crosswise, leastwise, likewise, nowise, otherwise, slantwise, in which -wise has the appearance of a suffix, and, in so far as it could or can still be freely combined with an adjective or a noun (as in senses 1b, 5b), it has actually performed the function of a suffix. The free use of the various forms, i.e. apart from the established simple words, is now only archaic except in sense 5b.
So something like in like wise became likewise, and with the influence of words like it, -wise was perceived as a suffix.
The noun wise meaning "manner" and the adjective wise meaning "sound judgment* are close in form and history. In Word Hoard, Old English scholar Stephen Barney records "wīs (adj) 'WISE' " right before "wīse (wk.f., and suffix) 'manner, way' " in the word group 29 headed by witan ("know"). They also have similar form in nearby and previous languages to Old English. Compare the adjective wise meaning sound of judgment, as adopted from the OED "wise, adj. (n.3 and adv.)":
Old English wís = Old Frisian, Old Saxon, Old High German (Middle Low German, Middle Dutch, Middle High German) wîs , (Dutch wijs , German weis in phrase einen weis machen ), Old Norse víss (Swedish, Danish vis ), Gothic weis (in compounds) < Old Germanic *wīsaz < pre-Germanic *wīttos , < Indo-European weid- (see wit v.1) + participial suffix -to-.
to wise meaning manner or way, which influenced -wise (OED again):
Old English wíse weak feminine (rarely wís strong feminine) manner, mode, condition, thing, affair, cause, reason, (occasionally) song = Old Frisian wîs , Old Saxon wîsa weak and strong (Middle Low German wîse , wîs , Middle Dutch wîze , wijs , Dutch wijze ), Old High German wîsa , and wîs manner, custom, tune (Middle High German wîse , German weise ), Old Norse vísa weak feminine stanza, *vís manner in öðruvís otherwise (Swedish visa , Danish vise song; also Swedish, Danish vis way, manner) < Old Germanic *wīsōn- , *wīsō : < wit- wit v.1 (for the sense compare the cognate Greek εἶδος form, shape, kind, state of things, course of action).
From Middle Low German wîs to close pairings in Old Norse, Dutch, and other languages, these would have been distinct but closely related words back to at least Old Germanic, and it's possible people have interchanged the two words and meanings. However, in English, -wise is not directly related to the wise in "a wise person."
Apparently the divergence in meaning was very early. etymonline.com lists a noun sense of wise that provides the origin of the modern suffix:
"way of proceeding, manner," Old English wise "way, fashion, custom, habit, manner; condition, state, circumstance," from Proto-Germanic *wison "appearance, form, manner" (see wise (adj.)). Compare Old Saxon wisa, Old Frisian wis, Danish vis, Middle Dutch wise, Dutch wijs, Old High German wisa, German Weise "way, manner." Most common in English now as a word-forming element (as in likewise, clockwise); the adverbial -wise has been used thus since Old English.
These origins are different from the origin of the adjective sense referring to knowledge, which comes from Proto-Germanic *wissaz.
However it does hint at an earlier common derivation:
For sense evolution from "to see" to "way of proceeding," compare cognate Greek eidos "form, shape, kind," also "course of action." Ground sense is "to see/know the way."