In terms of British footballers the description has been loosely and recklessly used to describe players who were nowhere near that level - not even Kenny Dalglish or Graeme Souness. International class yes, by all means, but neither were even remotely in Baxter's league. Dennis Law perhaps, and George Best certainly, but not many more.
Jim Baxter played for Raith Rovers, Sunderland and Nottingham Forest - but he will always be remembered as Jim Baxter of Rangers.
He joined the Ibrox club in the summer of 1960 for a transfer fee of £17,500 from Raith Rovers – a substantial sum by the standards of the day, but a mere pittance compared with the fees paid today for players not fit to lace his boots.
Baxter's arrival was the catalyst that transformed a moderate Rangers side into one that swept the boards in Scottish football for the next five years, winning three League Championships, three Scottish Cups and four League Cups.
Along the way the Light Blues reached one European final and two quarterfinals, advanced stages which today's superstars are light years from achieving.
He played in total 254 games for Rangers, scoring 24 goals. In his initial season at Ibrox the 'Gers swept all before them, playing an exciting brand of attacking football not seen in Scotland since before the war, and most certainly not seen since.
That line-up of Season 1960-61 can be recited by the fans of that era even today, forty years on: Ritchie; Shearer, Caldow; Davis. Paterson, Baxter; Scott, McMillan, Millar, Brand, Wilson.
Week after week it was the same eleven who played for Rangers - and Baxter was the epicentre, the playmaker, the creator. In today's parlance he was the midfield general. In any language he was a maestro, a genius.
He loved to play on the European stage - an 8-0 thrashing of Borussia Monchengladbach on a night of torrential rain at Ibrox, a royal performance in front of Prince Rainier of Monaco as Rangers overcame the French Champions on their own patch in September 1961, and like a matador against the Spaniards of Seville who were crushed 4-0.
Perhaps his finest hour in Europe came in the Prater Stadium, Vienna in December 1964 as Rangers overcame Rapid 2-0 to advance to the last eight of the European Champions' Cup. The Prater was one of the most hostile arenas in Europe in those days, yet 'Slim Jim' captivated the Austrian fans with his class before tragically breaking his leg in the dying minutes.
That broken leg perhaps cost Rangers the European Cup that season - as it was without Baxter they came so close to defeating the World Champions Inter Milan in the quarterfinal, losing 2-3 on aggregate. Jim Baxter won 34 caps for Scotland, 24 whilst with Rangers. A modest figure by today's standards - but in the early-60's the number of International fixtures was perhaps one-third the total of today.
His two appearances at Wembley are of course legendary - both goals in a 2-1 win in 1963, toying with the World Champions and playing 'keepy-uppy' in 1967. At Hampden in June 1966 he outshone even the great Pele as the then World Cup Holders Brazil visited.
Above all else however Baxter loved to play against Celtic - time and time again Rangers fans revelled in the defeat of their greatest rivals as Baxter toyed with the likes of Billy McNeill, Pat Crerand, and anyone else in green-and-white. Only twice did he suffer defeat in five years of 'Old Firm' games.
In the 1963 Scottish Cup Final Replay he mercilessly taunted Celtic in the last 25 minutes with Rangers 3-0 ahead, playing 'keepy-uppy', sitting on the ball, taking it for a walk.
Many Rangers fans to this day maintain that with Celtic on their knees Rangers should have gone for the jugular. Seven or even eight goals were there for the asking, revenge for other defeats. Perhaps they were right, but that was never Baxter's style.
Rangers were never the same after Jim Baxter left in the summer of 1965 - how could they replace a genius?
Had Baxter stayed the history of Scottish football over the next ten years would surely have been infinitely different - but the Ibrox Board at that time would not pay the money.
He returned to Rangers in 1969 - but the magic was only there intermittently. Years of living life to the full had finally taken their toll, although there was still enough of the old class left for him to engineer a 2-1 defeat of Celtic at Ibrox in August 1969.
His retiral at the age of just 30 in 1970 was a criminal waste of talent.
Jim Baxter left us on Saturday 14 April, 2001 at 6.30pm. The greatest player of his generation - to many the greatest player of any generation - Baxter passed away at the age of just 61, a tragic loss at such an early age.
We shall not see his like again.