Yes, the Bolts do look very much alike.
Both rifles are members of the LEE-ENFIELD family.
They are descended from the original 1879 LEE Rifle. James Paris LEE was a Scots-Canadian working in the USA who had some really advanced ideas about gunmaking. He designed the first ####-on-close bolt rifle with a BOX MAGAZINE under the boltway. He was having a batch of rifles made by SHARPS' when SHARPS' went broke. REMINGTON bought out much of the tooling, along with the parts for which Lee had paid, at the bankruptcy sale. Remington looked at the rifle, made a deal with Lee: in return for finishing Lee's rifles, Remington would take over the design, pay Lee a royalty on sales and give Lee a job as a salesman. The US Navy bought 500 of the 1879 rifles in .45-70 calibre and the British Government bought one of those and a couple in .43 Spanish..... and took them to ENFIELD where they were developed into the new rifle which was adopted in 1888 as the standard rifle for one-quarter of the world.
The Mark III* model is a mid-World-War-One modification of the previous (1907) Mark III Short rifle to permit faster manufacture. THIS rifle was renamed the Number 1 Rifle in 1927.
The Number 4 Rifle is a 1931 redesign of the LEE-ENFIELD type to correct what were seen as deficiencies in the earlier rifles and to permit even FASTER manufacture.
They are very similar in APPEARANCE but there are also huge differences, some of them not readily seen. As one example, the THREADS on the Number 4 all are BA System threads, while threads on the Number 1 are ENFIELD System. Bolt-heads do NOT swap back and forth and the quickest way to identify which bolt is for which rifle is to look at the HEAD when it is screwed on; if the Head has a LIP on its underside, it is for a Number 1 (the SMLE or "Smellie") whereas if it has a thin SLOT on its right-hand side, it is for a Number 4 or a Number 5 (the "Jungle Carbine"). Interesting enough, the Number 4 Rifle has NO nickname, never has had one; it has always been the "Number 4 Rifle".
But, stripped down, they look so very much alike that you had BETTER have gauges!